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It also includes composite situations such as conical caps, tents/tombs, and canvas length/area derived from cone geometry.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/surface-area-and-volume-of-a-right-circular-cone-201/297424/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/surface-area-and-volume-of-a-right-circular-cone-201/297424.png","ImageObject",300,407,{"name":42,"@type":43},"Chloe Bennett","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-26","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"Which formula is used for the curved surface area of a right circular cone?","Question",{"text":63,"@type":64},"The curved surface area is given by CSA = π r l, where r is the radius of the base and l is the slant height.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find the slant height when radius and height are given?",{"text":68,"@type":64},"Use Pythagoras’ theorem: l = √(r² + h²), since the slant height forms the hypotenuse of a right triangle.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you compute the total surface area of a cone?",{"text":72,"@type":64},"Total surface area = curved surface area + area of the base = π r l + π r².","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},297424,1790219874,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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= 60cm  \nWKT, Curved surface area of a cone = π rl  \n∴ Curved surface area = ~~ ~~227 × 21 × 60  \n= 3960cm2  \n2.  \nSol:  \nGiven,  \nRadius of a cone = 12cm = h  \nHeight of a cone = 12cm = h  \nSlant height of the cone = r 2 + h2  \n= 52 +122  = 13cm  \n∴ Curved surface Area = π rl  \n= ~~ ~~227 × 5 × 12  \n= 204 ⋅ 28cm2  \n3.  \nSol:  \nGiven  \nRadius of a cone ( r ) = 7cm.  \nLet ' l ' be the slant height of a cone  \n∴ Curved surface area = π rl.  \n⇒ 176 = π × 7 × l  \n⇒ l = 176 = 176 × 7 = 8cm.  \n7π 7 × 22  \n4.  \nSol:  \nGiven that  \nSlant height ‘l’ = 28m.  \nHeight of cone ( h ) = 21cm  \n∴Radius of cone ( r ) = 252 − 212  [by Pythagoras theorem]  \n= 77cm  \n∴Area of base = π r2  \n= ~~ ~~227 × ( 77~~ ~~ )2  \n= ~~ ~~227 × 7 × 7 × 7 = 1078cm2 .  \n5.  \nSol:  \nWKT, Total surface area = π rl + π r2  \nNow l = h2 + r 2  [by Pythagoras theorem]  \nHere, given  \nRadius = 6cm and height = 8cm  \n⇒ length = 62 + 82  \n= 10cm  \n∴ Total surface area = π rl + π r2 = 􀂧􀂨􀂩 ~~ ~~227 × 6 × 10􀂷􀂹􀂸 + 􀂨􀂧􀂩 ~~ ~~227 × 6 × 6􀂷􀂹􀂸= 􀂧􀂨􀂩 ~~ ~~13270~~ ~~ 􀂷􀂹􀂸 + ~~ ~~7972 = 301⋅ 71cm2  \n6.  \nSol:  \nGiven that,  \nRadius of a base of a cone = 5 ⋅ 25cm  \nSlant height of cone = 10cm  \nCurved surface area of cone = π rl  \n= ~~ ~~227 × 5 ⋅ 25 × 10cm2  \n= ( 22 × 0 ⋅75 × 10 ) cm2  \n= 165cm2  \nThus, the curved surface area of a cone is 165cm2  \n7.  \nSol:  \nGiven that,  \nRadius of base of cone = 􀂧􀂨􀂩 ~~ ~~242􀂷􀂹􀂸 = 12m Slant height of cone = 21m.  \nTotal surface area of cone = π r2 +π rl  \n= π r ( r + l )  \n= ~~ ~~227 × 12 × ( 12 + 21)  \n= ~~ ~~227 × 12 × 33m2  \n= 1244 ⋅57m2 .  \n8.  \nSol:  \nGiven that  \nCurved surface area of cone = 60πcm2  \n∴Slant height of cone ( l ) = 8cm. i.e., π rl = 60π  \n⇒ π × r × 8 = 60π 60  \n⇒ r = ~~ ~~ = 7 ⋅5 8  \n∴Radius of cone = 7 ⋅5cm.  \n9.  \nSol:  \nGiven diameter = 70cm  \n⇒ 2r = 70cm  \n⇒ r = 35cm  \nNow, curved surface area = 4070cm2  \n⇒ π rl = 4070  \nWhere r = radius of the cone  \nl = slant height of the cone  \n∴ π rl = 4070  \n⇒ ~~ ~~227 × 35 × l = 4070  \n⇒ l =  4070 × 7 = 37cm  \n22 × 35  \n∴ Slant height of the cone = 37cm.  \n10.  \nSol:  \nGiven that,  \nCurved surface area = π rl = 792.  \nLet the radius ( r ) = 4x  \nHeight ( h ) = 7x  \nNow, CSA = 792  \n227 × 4x× 7x = 792  \n⇒ 88x2 = 792  \n2 792  \n⇒ x =  88  = 9.  \n⇒ x = 3.  \n∴Radius = 4x = 4 × 3 = 12cm.  \n11.  \nSol:  \nGiven that,  \nRadius of conical cap ( r ) = 7cm.  \nHeight of conical cap ( h ) = 24cm.  \nSlant height (I) of conical cap = r 2 + h2  \n= ( 7 )2 + ( 24 )2 cm  \n= 25cm  \nCSA of 1 conical cap = π rl =  22 × 7 × 25 cm2 = 550cm2  \nCurved surface area of 0 such 10 conical caps = 5500cm2 [􀀧550× 10]  \nThus, 5500cm2 sheet will be req for making of 10 caps.  \n12.  \nSol:  \nGiven that,  \nDiameter of two cones area equal  \n∴ Their radius are equal Let r1 = r2 = r Let ratio be x  \n∴ Slant height l1 of 1st cone = 4x  \nSimilarly slant height l2 of 2nd cone = 3x.  \nC ⋅ S A1   π r1l1   π × r × 4x   4  \n∴ C ⋅ S A2 = π r2l2 = π × r × 3x = 3 .  \n13.  \nSol:  \nLet curved surface area off 1st cone = 2x  \nCSA of 2nd cone = x  \nand slant height of 1st cone = h  \nand slant height of 2nd cone = 2h  \n CSA of 1st cone   2x   2  \n∴ = =  \nCSA of 2nd cone x 1 .  \nπ r1l1 2  \n⇒ ~~ ~~ = ~~ ~~  \nπ r2l2 1  \nr1h 2 r1 4  \n⇒ ~~ ~~ =  ⇒ ~~ ~~ = ~~ ~~ .  \nr2 h 1 r2 1  \ni.e., ratio of r1 and r2 is ( 4 :1)  \n14.  \nSol:  \nGiven that,  \nDiameters of two cones are equal  \n∴ Their radius are also equal i.e., r1 = r2  \nLet the ratio of slant height be x  \n∴ l1 = 5x and l2 = 4x  \n∴Ratio of curved surface area =  C1  \nC2  \nC1 π r1l1 π r1Sx 5  \n∴  C2  =  π r2l2  =  π r2 ( 4x) =  4  \n∴Ratio of curved surface area = 5: 4  \n15.  \nSol:  \n(i) Given that,  \nSlant height of cone = 14cm  \nLet radius of circular end of cone = r.  \nCurved surface area of cone = π rh  \n308cm2 = 􀂧􀂨􀂩 ~~ ~~227 × r × 14􀂷􀂹􀂸 cm 􀀧CSA = 308cm2 ) 308  \n⇒ r = ~~ ~~ cm = 7cm  \n44  \nThus, radius of circular end of cone = 7cm  \n(ii) Given that CSA = 308cm2  \nWKT, ","cbCailQalNkmvWfF","https://ap.wps.com/l/cbCailQalNkmvWfF","pdf",843025,18,"English","# Surface Area and Volume Calculations for a Right Circular Cone\n## Curved surface area and total surface area\n## Pythagoras theorem for slant height\n## Applications: conical caps, tents, and canvas/cost problems","[{\"question\":\"Which formula is used for the curved surface area of a right circular cone?\",\"answer\":\"The curved surface area is given by CSA = π r l, where r is the radius of the base and l is the slant height.\"},{\"question\":\"How do you find the slant height when radius and height are given?\",\"answer\":\"Use Pythagoras’ theorem: l = √(r² + h²), since the slant height forms the hypotenuse of a right triangle.\"},{\"question\":\"How do you compute the total surface area of a cone?\",\"answer\":\"Total surface area = curved surface area + area of the base = π r l + π r².\"}]","Surface Area and Volume of a Right Circular Cone - 20.1 | PDF",1789744403,45]