{"id":155688,"date":"2022-03-26T00:55:25","date_gmt":"2022-03-25T19:25:25","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/surface-area-of-cylinder-introduction-formulae-derivation-solved-examples-faqs\/"},"modified":"2025-05-29T10:29:06","modified_gmt":"2025-05-29T04:59:06","slug":"surface-area-of-cylinder-introduction-formulae-derivation-solved-examples-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/surface-area-of-a-cylinder\/","title":{"rendered":"Total Surface Area of Cylinder &#8211; Introduction, Formulae, Derivation, Solved Examples &#038; FAQs"},"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\/maths\/surface-area-of-a-cylinder\/#Surface_Area_of_Cylinder\" title=\"Surface Area of Cylinder\">Surface Area of Cylinder<\/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\/maths\/surface-area-of-a-cylinder\/#Curved_Surface_Area_CSA_of_Cylinder\" title=\"Curved Surface Area (CSA) of Cylinder\">Curved Surface Area (CSA) of Cylinder<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/surface-area-of-a-cylinder\/#Total_Surface_Area_TSA_of_Cylinder\" title=\"Total Surface Area (TSA) of Cylinder\">Total Surface Area (TSA) of Cylinder<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/surface-area-of-a-cylinder\/#Derivation_of_the_Formula_of_Surface_Area_of_Cylinder\" title=\"Derivation of the Formula of Surface Area of Cylinder\">Derivation of the Formula of Surface Area of Cylinder<\/a><\/li><\/ul><\/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\/maths\/surface-area-of-a-cylinder\/#Solved_Examples\" title=\"Solved Examples\">Solved Examples<\/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\/maths\/surface-area-of-a-cylinder\/#FAQs\" title=\"FAQs\">FAQs<\/a><\/li><\/ul><\/nav><\/div>\n<p><span style=\"color: #0000ff;\"><strong>Total Surface Area of Cylinder:<\/strong><\/span> A cylinder is a geometric figure formed by two parallel planes intersecting in a straight line. The planes are called the bases of the cylinder, and the line that intersects is called the cylinder&#8217;s axis. The space between the two bases is called the cylinder&#8217;s volume.<\/p>\n<p>A cylinder&#8217;s surface area is the total area of all the surfaces that make up the cylinder. The surface area of a cylinder is made up of the areas of the cylinder&#8217;s two bases and the area of its curved surface. The area of a base is the product of its length and width. The area of a curved surface is the product of its height and circumference.<\/p>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Surface_Area_of_Cylinder\"><\/span>Surface Area of Cylinder<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The surface area of a cylinder is the total area of all the surfaces of the cylinder. The surface area of a cylinder is calculated by multiplying the length of the cylinder by the width of the cylinder by the height of the cylinder.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Curved_Surface_Area_CSA_of_Cylinder\"><\/span>Curved Surface Area (CSA) of Cylinder<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A cylinder is solid with two parallel circular bases. The curved surface area of a cylinder is the sum of the areas of the two circular bases and the area of the curved surface between them.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Total_Surface_Area_TSA_of_Cylinder\"><\/span>Total Surface Area (TSA) of Cylinder<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>= \u03c0 \u00d7 radius of cylinder \u00d7 height of the cylinder<\/p>\n<p>= \u03c0 \u00d7 2 cm \u00d7 5 cm<\/p>\n<p>= \u03c0 \u00d7 10 cm<\/p>\n<p>= 31.4 cm<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Derivation_of_the_Formula_of_Surface_Area_of_Cylinder\"><\/span>Derivation of the Formula of Surface Area of Cylinder<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul style=\"list-style-type: square;\">\n<li>The surface area of a cylinder is the sum of the surface areas of the two circular bases and the surface area of the cylindrical body.<\/li>\n<li>The surface area of a circular base is \u03c0r\u00b2.<\/li>\n<li>The surface area of a cylindrical body is \u03c0rL.<\/li>\n<li>The surface area of a cylinder is \u03c0r\u00b2+\u03c0rL.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Examples\"><\/span>Solved Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Example 1: Find the total surface area of a cylinder with a radius of 7 cm and a height of 14 cm.<\/p>\n<p>Solution:<\/p>\n<p>The formula for the total surface area of a cylinder is given as:<br \/>\nTotal surface area = 2\u03c0r(r + h)<\/p>\n<p>Where r is the radius of the base of the cylinder, and h is the height of the cylinder.<\/p>\n<p>Substituting the given values, we get:<br \/>\nTotal surface area = 2\u03c0(7)(7 + 14)<br \/>\nTotal surface area = 2\u03c0(7)(21)<br \/>\nTotal surface area = 294\u03c0<br \/>\nTotal surface area \u2248 922.98 cm\u00b2<\/p>\n<p>Therefore, the total surface area of the cylinder is approximately 922.98 cm\u00b2.<\/p>\n<p>Example 2: A cylindrical drum has a diameter of 1.2 m and a height of 2.4 m. Calculate the total surface area of the drum.<\/p>\n<p>Solution:<\/p>\n<p>First, we need to find the radius of the base of the cylinder. The diameter is given as 1.2 m, so the radius is half of that, which is 0.6 m.<\/p>\n<p>Using the formula for the total surface area of a cylinder, we get:<br \/>\nTotal surface area = 2\u03c0r(r + h)<\/p>\n<p>Substituting the given values, we get:<br \/>\nTotal surface area = 2\u03c0(0.6)(0.6 + 2.4)<br \/>\nTotal surface area = 2\u03c0(0.6)(3)<br \/>\nTotal surface area = 3.6\u03c0<br \/>\nTotal surface area \u2248 11.31 m\u00b2<\/p>\n<p>Therefore, the total surface area of the cylindrical drum is approximately 11.31 m\u00b2.<\/p>\n<p>Example 3: A cylindrical water tank has a radius of 3 m and a height of 8 m. Calculate the cost of painting the tank if the cost of painting 1 m\u00b2 is $5.<\/p>\n<p>Solution:<\/p>\n<p>To find the cost of painting the cylindrical tank, we need to first find its total surface area using the formula:<br \/>\nTotal surface area = 2\u03c0r(r + h)<\/p>\n<p>Substituting the given values, we get:<br \/>\nTotal surface area = 2\u03c0(3)(3 + 8)<br \/>\nTotal surface area = 2\u03c0(3)(11)<br \/>\nTotal surface area = 66\u03c0<br \/>\nTotal surface area \u2248 207.35 m\u00b2<\/p>\n<p>The cost of painting 1 m\u00b2 is given as $5, so the cost of painting 207.35 m\u00b2 is:<br \/>\nCost = 207.35 \u00d7 5<br \/>\nCost = $1036.75<\/p>\n<p>Therefore, the cost of painting the cylindrical water tank is $1036.75.<\/p>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Q: What is the Total Surface Area of a Cylinder?<br \/>\nA: The Total Surface Area of a Cylinder is the sum of the areas of its curved surface and two circular bases.<\/p>\n<p>Q: What is the formula for the Total Surface Area of a Cylinder?<br \/>\nA: The formula for the Total Surface Area of a Cylinder is 2\u03c0r(h + r), where r is the radius of the base and h is the height of the cylinder.<\/p>\n<p>Q: How do you find the curved surface area of a cylinder?<br \/>\nA: The curved surface area of a cylinder is the product of its height and the circumference of its base, which is 2\u03c0r.<\/p>\n<p>Q: How do you find the area of the two circular bases of a cylinder?<br \/>\nA: The area of each circular base of a cylinder is \u03c0r^2, where r is the radius of the base.<\/p>\n<p>Q: What is the unit of measurement for Total Surface Area of a Cylinder?<br \/>\nA: The unit of measurement for Total Surface Area of a Cylinder is square units, such as square meters or square centimeters.<\/p>\n<p>Q: Can the height and radius of a cylinder be the same?<br \/>\nA: Yes, the height and radius of a cylinder can be the same. In that case, the cylinder is called a &#8220;right circular cylinder.&#8221;<\/p>\n<p>Q: What are the applications of the Total Surface Area of a Cylinder in real life?<br \/>\nA: The Total Surface Area of a Cylinder is used in many fields, such as architecture, engineering, and manufacturing, to calculate the amount of material needed to create cylindrical objects like pipes, tanks, and columns.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Total Surface Area of Cylinder: A cylinder is a geometric figure formed by two parallel planes intersecting in a straight [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Total Surface Area of Cylinder","_yoast_wpseo_title":"Total Surface Area of Cylinder - Introduction, Formulae | Infinity Learn","_yoast_wpseo_metadesc":"Learn about the Total Surface Area of Cylinder in detail on infinitylearn.com. 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