{"id":26910,"date":"2022-01-31T11:45:25","date_gmt":"2022-01-31T06:15:25","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=26910"},"modified":"2024-01-10T13:04:47","modified_gmt":"2024-01-10T07:34:47","slug":"surface-areas-and-volumes-class-10-notes-maths-chapter-13","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-10\/maths\/surface-areas-and-volumes-class-10-notes-maths-chapter-13\/","title":{"rendered":"Surface Areas and Volumes Class 10 Notes Maths Chapter 13"},"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\/study-material\/cbse-notes\/class-10\/maths\/surface-areas-and-volumes-class-10-notes-maths-chapter-13\/#CBSE_Class_10_Maths_Notes_Chapter_13_Surface_Areas_and_Volumes\" title=\"CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes\">CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-10\/maths\/surface-areas-and-volumes-class-10-notes-maths-chapter-13\/#NCERT_Notes_for_Class_10_Maths\" title=\"NCERT Notes for Class 10 Maths\">NCERT Notes for Class 10 Maths<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class_10_Maths_Notes_Chapter_13_Surface_Areas_and_Volumes\"><\/span>CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46895780274_b97dbdddf6_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 1\" width=\"742\" height=\"861\" \/><\/p>\n<p><strong>SURFACE AREA AND VOLUME OF COMBINATIONS<\/strong><\/p>\n<p><strong>Cone on a Cylinder.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46895779634_916e089647_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 2\" width=\"129\" height=\"168\" \/><br \/>\nr = radius of cone &amp; cylinder;<br \/>\nh<sub>1<\/sub> = height of cone<br \/>\nh<sub>2<\/sub> = height of cylinder<br \/>\nTotal Surface area = Curved surface area of cone + Curved surface area of cylinder + area of circular base<br \/>\n= \u03c0rl + 2\u03c0rh<sub>2<\/sub> +\u03c0r<sup>2<\/sup>;<br \/>\nSlant height, l = \\(\\sqrt { { r }^{ 2 }+{ { { h }_{ 1 }^{ 2 } } } }\\)<br \/>\nTotal Volume = Volume of cone + Volume of cylinder<br \/>\n= \\(\\frac { 1 }{ 3 } { \\pi r }^{ 2 }{ h }_{ 1 }+{ \\pi r }^{ 2 }{ h }_{ 2 }\\)<\/p>\n<p><strong>Cone on a Hemisphere:<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46895779564_4ef97806fe_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 3\" width=\"128\" height=\"163\" \/><br \/>\nh = height of cone;<br \/>\nl = slant height of cone = \\(\\sqrt { { r }^{ 2 }+{ h }^{ 2 } }\\)<br \/>\nr = radius of cone and hemisphere<br \/>\nTotal Surface area = Curved surface area of cone + Curved surface area of hemisphere = \u03c0rl + 2\u03c0r<sup>2<\/sup><br \/>\nVolume = Volume of cone + Volume of hemisphere = \\(\\frac { 1 }{ 3 } { \\pi r }^{ 2 }h+\\frac { 2 }{ 3 } { \\pi r }^{ 3 }\\)<\/p>\n<p><strong>Conical Cavity in a Cylinder<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46704525795_83034c6081_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 4\" width=\"140\" height=\"137\" \/><br \/>\nr = radius of cone and cylinder;<br \/>\nh = height of cylinder and conical cavity;<br \/>\nl = Slant height<br \/>\nTotal Surface area = Curved surface area of cylinder + Area of bottom face of cylinder + Curved surface area of cone = 2\u03c0rh + \u03c0r<sup>2<\/sup> + \u03c0rl<br \/>\nVolume = Volume of cylinder \u2013 Volume of cone = \\({ \\pi r }^{ 2 }h-\\frac { 1 }{ 3 } { \\pi r }^{ 2 }h=\\frac { 2 }{ 3 } { \\pi r }^{ 2 }h\\)<\/p>\n<p><strong>Cones on Either Side of Cylinder.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46895779464_4ebfb013ce_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 5\" width=\"195\" height=\"127\" \/><br \/>\nr = radius of cylinder and cone;<br \/>\nh<sub>1<\/sub> = height of cylinder<br \/>\nh<sub>2<\/sub> = height of cones<br \/>\nSlant height of cone, l = \\(\\sqrt { { h }_{ 2 }^{ 2 }+{ r }^{ 2 } }\\)<br \/>\nSurface area = Curved surface area of 2 cones + Curved surface area of cylinder = 2\u03c0rl + 2\u03c0rh<sub>1<\/sub><br \/>\nVolume = 2(Volume of cone) + Volume of cylinder = \\(\\frac { 2 }{ 3 } { \\pi r }^{ 2 }{ h }_{ 2 }+{ \\pi r }^{ 2 }{ h }_{ 1 }\\)<\/p>\n<p><strong>Cylinder with Hemispherical Ends.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46895779174_302b9bc7da_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 6\" width=\"196\" height=\"98\" \/><br \/>\nr = radius of cylinder and hemispherical ends;<br \/>\nh = height of cylinder<br \/>\nTotal surface area= Curved surface area of cylinder + Curved surface area of 2 hemispheres = 2\u03c0rh + 4\u03c0r<sup>2<\/sup><br \/>\nVolume = Volume of cylinder + Volume of 2 hemispheres = \\({ \\pi r }^{ 2 }h+\\frac { 4 }{ 3 } { \\pi r }^{ 3 }\\)<\/p>\n<p><strong>Hemisphere on Cube or Hemispherical Cavity on Cube<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46895779124_07b04d4411_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 7\" width=\"149\" height=\"127\" \/><br \/>\na = side of cube;<br \/>\nr = radius of hemisphere.<br \/>\nSurface area = Surface area of cube \u2013 Area of hemisphere face + Curved surface area of hemisphere<br \/>\n= 6a<sup>2<\/sup> \u2013 \u03c0r<sup>2<\/sup> + 2\u03c0r<sup>2<\/sup> = 6a<sup>2<\/sup> + \u03c0r<sup>2<\/sup><br \/>\nVolume = Volume of cube + Volume of hemisphere = \\({ a }^{ 3 }+\\frac { 4 }{ 3 } { \\pi r }^{ 3 }\\)<\/p>\n<p><strong>Hemispherical Cavity in a Cylinder<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/46704524665_d11194d6fd_o.png\" alt=\"Surface Areas and Volumes Class 10 Notes Maths Chapter 13 8\" width=\"140\" height=\"140\" \/><br \/>\nr = radius of hemisphere;<br \/>\nh = height of cylinder<br \/>\nTotal surface area = Curved surface area of cylinder + Surface area of base + Curved surface area of hemisphere<br \/>\n= 2\u03c0rh + \u03c0r<sup>2<\/sup> + 2\u03c0r<sup>2<\/sup> = 2\u03c0rh + 3\u03c0r<sup>2<\/sup><br \/>\nVolume = Volume of cylinder \u2013 Volume of hemisphere = \\({ \\pi r }^{ 2 }h-\\frac { 2 }{ 3 } { \\pi r }^{ 3 }\\)<\/p>\n<div class=\"featured-snippet\">\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Notes_for_Class_10_Maths\"><\/span>NCERT Notes for Class 10 Maths<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>Chapter 1 Real Numbers Class 10 Notes<\/li>\n<li>Chapter 2 Polynomials Class 10 Notes<\/li>\n<li>Chapter 3 Pair of Linear equations in Two Variables Class 10 Notes<\/li>\n<li>Chapter 4 Quadratic Equations Class 10 Notes<\/li>\n<li>Chapter 5 Arithmetic Progressions Class 10 Notes<\/li>\n<li>Chapter 6 Triangles Class 10 Notes<\/li>\n<li>Chapter 7 Coordinate Geometry Class 10 Notes<\/li>\n<li>Chapter 8 Introduction to Trigonometry Class 10 Notes<\/li>\n<li>Chapter 9 Some Applications of Trigonometry Class 10 Notes<\/li>\n<li>Chapter 10 Circles Class 10 Notes<\/li>\n<li>Chapter 11 Constructions Class 10 Notes<\/li>\n<li>Chapter 12 Areas related to Circles Class 10 Notes<\/li>\n<li>Chapter 13 Surface Areas and Volumes Class 10 Notes<\/li>\n<li>Chapter 14 Statistics Class 10 Notes<\/li>\n<li>Chapter 15 Probability Class 10 Notes<\/li>\n<\/ul>\n<\/div>\n<p>We hope the given CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes Pdf free download will help you. If you have any query regarding NCERT Class 10 Maths Notes Chapter 13 Surface Areas and Volumes, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes SURFACE AREA AND VOLUME OF COMBINATIONS Cone on [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Get Surface Areas and Volumes Class 10 Notes Maths Chapter 13 on Infinity Learn.","custom_permalink":"study-material\/cbse-notes\/class-10\/maths\/surface-areas-and-volumes-class-10-notes-maths-chapter-13\/"},"categories":[92,13,21],"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>Surface Areas and Volumes Class 10 Notes Maths Chapter 13 - 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