{"id":623029,"date":"2023-06-20T22:36:22","date_gmt":"2023-06-20T17:06:22","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=623029"},"modified":"2025-02-28T16:30:59","modified_gmt":"2025-02-28T11:00:59","slug":"area-of-a-sector-of-a-circle-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/","title":{"rendered":"Area of A Sector of A Circle Formula\u00a0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#What_is_Area_of_Sector_of_a_Circle\" title=\"What is Area of Sector of a Circle?\">What is Area of Sector of a Circle?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#Sector_Definition\" title=\"Sector Definition \">Sector Definition <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#Area_of_Sector_Formula\" title=\"Area of Sector Formula \">Area of Sector Formula <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#Area_of_Sector_Formula_Derivation\" title=\"Area of Sector Formula Derivation \">Area of Sector Formula Derivation <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#Real-Life_Example_of_Area_of_Sector_of_Circle\" title=\"Real-Life Example of Area of Sector of Circle \">Real-Life Example of Area of Sector of Circle <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#Solved_Examples_on_Area_of_a_Sector_of_a_Circle\" title=\"Solved Examples on Area of a Sector of a Circle  \">Solved Examples on Area of a Sector of a Circle  <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#Frequently_Asked_Questions_on_Area_of_a_Sector_of_a_Circle\" title=\"Frequently Asked Questions on Area of a Sector of a Circle \">Frequently Asked Questions on Area of a Sector of a Circle <\/a><\/li><\/ul><\/nav><\/div>\n<p><b><span data-contrast=\"auto\">Introduction to Area Of A Sector Of A Circle Formula<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The area of sector of a circle is the space enclosed within the boundary of the sector. A sector always originates from the center of the circle. Let us learn more about the area of sector formula, and how to find the area of a sector in radians and degrees.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Area_of_Sector_of_a_Circle\"><\/span>What is Area of Sector of a Circle?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">The space enclosed by the sector of a circle is called the area of the sector. For example, a pizza slice is an example of a sector that represents a fraction of a pizza. There are two types of sectors: minor and major sectors. A minor sector is a sector that is less than a semi-circle, whereas, a major sector is a sector greater than a semi-circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> The figure given below represents the sectors in a circle. The shaded region shows the area of the sector OAPB. Here, \u2220AOB is the angle of the sector. It should be noted that the unshaded region is also a sector of the circle. So, the shaded region is the area of the minor sector and the unshaded region is the area of the major sector.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"><img loading=\"lazy\" class=\"size-medium wp-image-623038 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558-300x277.png\" alt=\"\" width=\"300\" height=\"277\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558-300x277.png?v=1687280772 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558.png?v=1687280772 439w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/> <\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span data-contrast=\"auto\">Now, let us learn about the area of a sector formula and its derivation after learning about the definition of a sector.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Sector Definition<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">The sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them. It is considered as a portion of a circle with two radii and an arc. A circle is divided into two sectors, the minor sector and the major sector where the minor sector is the smaller portion in the circle and the larger sector is the major portion. The semi-circle is the most common sector of a circle, which represents half a circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Area of Sector Formula<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">In order to find the total space enclosed by the sector, we use the area of a sector formula. The area of a sector can be calculated using the following formulas,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">Area of a Sector of Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, where, \u03b8 is the sector angle subtended by the arc at the center, in degrees, and &#8216;r&#8217; is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">Area of a Sector of Circle = 1\/2 \u00d7 r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">\u03b8, where, \u03b8 is the sector angle subtended by the arc at the center, in radians, and &#8216;r&#8217; is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ul>\n<h2><b><span data-contrast=\"auto\">Area of Sector Formula Derivation<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">Let us apply the unitary method to derive the formula for the area of the sector of a circle. We know that a complete circle measures 360\u00ba. The area of a circle with an angle measuring 360\u00ba at the center is given by \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, where &#8216;r&#8217; is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> If the angle at the center of the circle is 1\u00ba, the area of the sector is \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">\/360\u00ba. So, if the angle at the center is \u03b8, the area of the sector is, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, where,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">\u03b8 is the angle subtended at the center, given in degrees.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">r is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">In other words, \u03c0r<\/span><span data-contrast=\"auto\">2 <\/span><span data-contrast=\"auto\">represents the area of a full circle and \u03b8\/360\u00ba tells us how much of the circle is covered by the sector.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">If the angle at the center is \u03b8 in radians, then the formula for the area of the sector of a circle = (1\/2) \u00d7 r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">\u03b8, where, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"3\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">\u03b8 is the angle subtended at the center, given in radians.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"3\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">r is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">It should be noted that semi-circles and quadrants are special types of sectors of a circle with angles of 180\u00b0 and 90\u00b0 respectively.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Real-Life Example of Area of Sector of Circle<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">One of the most common real-life examples of the area of a sector is the slice of a pizza. The shape of the slices of a circular pizza is like a sector. Observe the figure given below that shows a pizza that is sectioned into 6 equal slices, where each slice is a sector, and the radius of the pizza is 7 inches. Now, let us find the area of the sector formed by each slice by using the sector area formula. It should be noted that since the pizza is divided into 6 equal slices, the angle of sector is 60\u00b0. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of Pizza slice = (\u03b8\/360\u00b0) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                 = (60\u00b0\/360\u00b0) \u00d7 (22\/7) \u00d7 72<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                 = 1\/6 \u00d7 22 \u00d7 7 <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                 = 77\/3<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                 = 25.67 square units.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Solved Examples on Area of a Sector of a Circle<\/span><\/b><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><b><span data-contrast=\"auto\">Example 1:<\/span><\/b><span data-contrast=\"auto\"> If the angle of a sector of a circle is 60\u00b0, and the radius of the circle is 7 inches, what is the area of the sector of this circle?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The radius of the circle is 7 inches and the angle is 60\u00b0. So, let us use the area of sector formula. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The area of sector = (\u03b8\/360\u00b0) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                  = (60\u00b0\/360\u00b0) \u00d7 (22\/7) \u00d7 72 <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                  = 77\/3 = 25.67 square units. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Therefore, the area of the minor sector is 25.67 square units.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 2:<\/span><\/b><span data-contrast=\"auto\"> An umbrella has equally spaced 8 ribs. If viewed as a flat circle of radius 7 units, what would be the area between two consecutive ribs of the umbrella? (Hint: The area between two consecutive ribs would form a sector of a circle)<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The radius of the flat umbrella = 7 units.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> There are 8 ribs in the umbrella. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Since a complete angle of a circle = 360\u00b0, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">the angle of each sector of the umbrella = 360\/8 = 45\u00b0 because the circle is divided into 8 equal sectors.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Thus, the area of secor = (\u03b8\/360\u00b0) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                       = (45\u00b0\/360\u00b0) \u00d7 22\/7 \u00d7 72<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                       = 77\/4 <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                                       = 19.25 square units.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Therefore, the area between two consecutive ribs of the umbrella is 19.25 square units.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 3: <\/span><\/b><span data-contrast=\"auto\">A circle with a diameter of 2 units is divided into 10 equal sectors. Can you find the area of each sector of the circle?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The diameter of the circle is 2 units, therefore, the radius of the circle is 1 unit. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Since a complete angle of a circle = 360\u00b0, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">the angle of each sector of the circle is 360\/10 = 36\u00b0 because the complete angle is divided into 10 equal parts. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of Sector = (\u03b8\/360\u00b0) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                           = 36\u00b0\/360\u00b0 \u00d7 22\/7 \u00d7 1 <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">                           = 11\/35 = 0.314 square units. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Therefore, the area of each sector of the circle is 0.314 square units. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Frequently Asked Questions on Area of a Sector of a Circle<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">1: What is the Area of a Sector of a Circle?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The space enclosed by the sector of a circle is called the area of the sector of a circle. The part of the circle that is enclosed by two radii and the corresponding arc is called the sector of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">2: What is the Formula for Area of Sector of Circle?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The two main formulas that are used to find the area of a sector are:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, where, \u03b8 is the angle subtended at the center, given in degrees, and &#8216;r&#8217; is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of Circle = 1\/2 \u00d7 r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">\u03b8, where, \u03b8 is the angle subtended at the center, given in radians, and &#8216;r&#8217; is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">3: How to Calculate Area of Sector using Degrees?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: When the angle subtended at the center is given in degrees, the area of a sector can be calculated using the following formula, area of a sector of circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, where, \u03b8 is the angle subtended at the center, given in degrees, and r is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4: What do you Mean by Sector of a Circle?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: A sector is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them. The semicircle is the most common sector of a circle, which represents half of a circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">5: What do you Mean by the Arc of a Circle?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: A part of a curve or a part of a circumference of a circle is called the arc. Many objects have a curve in their shape. The curved portion of these objects is mathematically referred to as an arc.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">6: How is the Area of Sector of Circle Formula Derived?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The area of the sector shows the area of a part of the circle&#8217;s area. We know that the area of a circle is calculated with the formula, \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">. The formula for the area of a sector of a circle is derived in the following way:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">7: Apply the unitary method to derive the formula of the area of a sector of circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: We know, a complete circle measures 360\u00ba. The area of a circle with an angle measuring 360\u00ba at the center is given by \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, where r is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">If the angle at the center of the circle is 1\u00ba, the area of the sector is \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">\/360\u00ba. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">So, if the angle at the center is \u03b8, the area of the sector is, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of a Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, where, \u03b8 is the angle subtended at the center, given in degrees, and r is the radius of the circle.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">In other words, \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> represents the area of a full circle and \u03b8\/360\u00ba tells us how much of the circle is covered by the sector.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">8: How to Find the Area of Sector with Arc Length and Radius?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The area of a sector can be calculated if the arc length and radius is given. We first calculate the angle (\u03b8) subtended by the arc with the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Length of Arc = (\u03b8\/360) \u00d7 2\u03c0r. Now, we already know the radius, and once the angle is known, the area of the sector can be calculated with the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of a Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">9:How to Find the Radius from Area of Sector?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: If the area of a sector is known, and the angle (\u03b8) subtended by the arc is known, the radius can be calculated by substituting the given values in the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of a Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">For example, let us find the radius if the area of a sector is 36\u03c0, and the sector angle is given as 90\u00b0. We will substitute the given values in the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of a Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">that is, 36\u03c0 = (90\/360) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">So, the value of r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> = 144, which means r = 12 units.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">10: How to Find the Area of Sector in Terms of Pi?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The area of sector can also be expressed in terms of pi (\u03c0). For example, if the radius of a circle is given as 4 units, and the angle subtended by the arc for the sector is 90\u00b0, let us find the area of the sector in terms of pi. Area of sector = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">. Substituting the values in the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of sector = (90\/360) \u00d7 \u03c0 \u00d7 4<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">After solving this, we get, the area as 4\u03c0.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">  <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">11: How to Find the Area of a Sector Without Angle?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: If the sector angle is not given, but we know the arc length and the radius, the area of a sector can be calculated. We first find the sector angle by substituting the given values of the arc length and radius in the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Length of Arc = (\u03b8\/360) \u00d7 2\u03c0r. After calculating the angle, we can easily find the area of the sector with the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a Sector of a Circle = (\u03b8\/360\u00ba) \u00d7 \u03c0r<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Area Of A Sector Of A Circle Formula The area of sector of a circle is the space [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Area of A Sector of A Circle Formula","_yoast_wpseo_title":"Area of A Sector of A Circle Formula with Examples - Infinity learn","_yoast_wpseo_metadesc":"Find the area of a sector of a circle with our simple formula. Learn to calculate this area given the radius and angle of the sector.","custom_permalink":"formulas\/area-of-a-sector-of-a-circle-formula\/"},"categories":[8438,8536],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Area of A Sector of A Circle Formula with Examples - Infinity learn<\/title>\n<meta name=\"description\" content=\"Find the area of a sector of a circle with our simple formula. Learn to calculate this area given the radius and angle of the sector.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Area of A Sector of A Circle Formula with Examples - Infinity learn\" \/>\n<meta property=\"og:description\" content=\"Find the area of a sector of a circle with our simple formula. Learn to calculate this area given the radius and angle of the sector.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-06-20T17:06:22+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-02-28T11:00:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558-300x277.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Ankit\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Area of A Sector of A Circle Formula with Examples - Infinity learn","description":"Find the area of a sector of a circle with our simple formula. Learn to calculate this area given the radius and angle of the sector.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/","og_locale":"en_US","og_type":"article","og_title":"Area of A Sector of A Circle Formula with Examples - Infinity learn","og_description":"Find the area of a sector of a circle with our simple formula. Learn to calculate this area given the radius and angle of the sector.","og_url":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2023-06-20T17:06:22+00:00","article_modified_time":"2025-02-28T11:00:59+00:00","og_image":[{"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558-300x277.png"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"Ankit","Est. reading time":"9 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#primaryimage","inLanguage":"en-US","url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558.png?v=1687280772","contentUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558.png?v=1687280772","width":439,"height":406},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/","name":"Area of A Sector of A Circle Formula with Examples - Infinity learn","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"primaryImageOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#primaryimage"},"datePublished":"2023-06-20T17:06:22+00:00","dateModified":"2025-02-28T11:00:59+00:00","description":"Find the area of a sector of a circle with our simple formula. Learn to calculate this area given the radius and angle of the sector.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Area of A Sector of A Circle Formula\u00a0"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d647d4ff3a1111ff8eeccdb6b12651cb"},"headline":"Area of A Sector of A Circle Formula\u00a0","datePublished":"2023-06-20T17:06:22+00:00","dateModified":"2025-02-28T11:00:59+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#webpage"},"wordCount":1803,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/area-of-a-sector-of-a-circle-formula\/#primaryimage"},"thumbnailUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223558-300x277.png","articleSection":["Formulas","Math Formulas"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d647d4ff3a1111ff8eeccdb6b12651cb","name":"Ankit","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/b1068bdc2711bd9c9f8be3b229f758f6?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/b1068bdc2711bd9c9f8be3b229f758f6?s=96&d=mm&r=g","caption":"Ankit"},"url":"https:\/\/infinitylearn.com\/surge\/author\/ankit\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/623029"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/53"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=623029"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/623029\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=623029"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=623029"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=623029"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=623029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}