[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297263-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297263-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","chapter-13-surface-areas-and-volumes-surfaces-tsalsa-cylinderconesphere-combined-figures","Chapter 13 - Surface Areas and Volumes - Surfaces, TSA/LSA, Cylinder/Cone/Sphere, Combined Figures","","Chapter 13 explains how to compute surface area and volume for common 3D solids using clear definitions and derived formulas. It covers cuboids (l, b, h), including total and lateral surface areas and the space diagonal, then cube relations. It derives cylinder surface area (curved and total) and volume, followed by right circular hollow cylinders. It presents cone curved and total surface area, sphere and hemisphere surface area and volume, then combines shapes to solve composite solids. It also includes frustum of a cone surface area and volume formulas.",{"@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/chapter-13-surface-areas-and-volumes-surfaces-tsalsa-cylinderconesphere-combined-figures/297263/",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/chapter-13-surface-areas-and-volumes-surfaces-tsalsa-cylinderconesphere-combined-figures/297263.png","ImageObject",300,407,{"name":42,"@type":43},"Noah","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",19,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the difference between surface area and volume for a solid?","Question",{"text":63,"@type":64},"Surface area is the sum of the areas of all faces of a solid. Volume is the space occupied by the solid object.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you calculate the total surface area and lateral surface area of a cuboid?",{"text":68,"@type":64},"For a cuboid with length l, breadth b, height h, TSA = 2(lb + bh + hl) and LSA = 2h(l + b), which excludes the top and bottom faces.",{"name":70,"@type":61,"acceptedAnswer":71},"What formulas are used for the surface area and volume of a cylinder?",{"text":72,"@type":64},"For radius r and height h, CSA = 2πrh and TSA = 2πrh + 2πr² = 2πr(h + r). Volume is V = πr²h.","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},297263,1789743445,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144},8796095462418,"https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780","Brain Builders Coaching Centre Lucknow Prepared By:Sachin Sir,9634156611  \nMATHEMATICS  \nChapter 13: Surface Areas and Volumes  \nSurface Areas and Volumes  \n1. Surface area of a solid is the sum of the areas of all its faces.  \n2. The space occupied by a solid object is the volume of that object.  \n3. If l, b, h denote respectively the length, breadth and height of a cuboid, then: Lateral surface area or Area of four walls = 2(ℓ + b) h  \nTotal surface area = 2(ℓb + bh + hℓ) Volume = ℓ × b × h  \nDiagonal of a cuboid =  \nSurface Area and Volume of Cuboid  \nA cuboid is the region covered by its six rectangular faces. The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.  \nSurface area of the cuboid  \nConsider a cuboid whose dimensions are l × b × h, respectively.  \nCuboid with length l, breadth b and height h  \nThe total surface area of the cuboid (TSA) = Sum of the areas of all its six faces TSA (cuboid) = 2(l × b) + 2(b × h) + 2(l × h) = 2(lb + bh + lh)  \nLateral surface area (LSA) is the area of all the sides apart from the top and bottom faces.  \nThe lateral surface area of the cuboid = Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC  \nLSA (cuboid) = 2(b × h) + 2(l × h) = 2h(l + b)  \nLength of diagonal of a cuboid =√(l 2 + b2 + h2 )  \n4. If the length of each edge of a cube is 'a' units, then: Lateral surface area = 4 × (edge)2  \nTotal surface area = 6 × (edge)2 Volume = (edge)3  \nDiagonal of a cube =√3 × edge  \nSurface Area and Volume of Cylinder  \nA cylinder is a solid shape that has two circular bases, connected with each other, through a lateral surface. Thus, there are three faces, two circular and one lateral, of a cylinder. Based on these dimensions, we can find the surface area and volume of a cylinder.  \nSurface Area of Cylinder  \nTake a cylinder of base radius r and height h units. The curved surface of this cylinder, if opened along the diameter (d = 2r) of the circular base can be transformed into a rectangle of length 2πr and height h units. Thus,  \nTransformation of a Cylinder into a rectangle.  \nCSA of a cylinder of base radius r and height h = 2π × r × h  \nTSA of a cylinder of base radius r and height h = 2π × r × h + area of two circular bases =2π × r × h + 2πr 2  \n=2πr (h + r)  \nVolume of a Cylinder  \nVolume of a cylinder = Base area × height = (πr2 ) × h = πr2 h  \nCylinder with height h and base radius r  \n5. If r and h respectively denote the radius of the base and the height of a right circular cylinder, then: Area of each end or Base area = 􀟨􀝎 2  \nArea of curved surface or lateral surface area = perimeter of the base x height = 2􀟨􀝎ℎ Total surface area (including both ends) = 2􀟨􀝎ℎ + 􀟨􀝎 2 + 2􀟨􀝎 (ℎ + 􀝎)  \nVolume = Area of the base × height = 􀟨􀝎2 ℎ  \n6. If R and r respectively denote the external and internal radii of a right circular hollow cylinder and h denotes its height, then:  \nArea of each end = 􀟨􀜴 2 − 􀟨􀝎 2  \nArea of curved surface = 2􀟨 (􀜴 + 􀝎)ℎ  \nTotal surface area = (Area of curved surface) + 2(Area of each end)= 2􀟨 (􀜴 + 􀝎)ℎ + (􀟨􀜴2 − 􀟨􀝎2 )  \n7. If r, h and l respectively denote the radius, height and slant height of a right circular cone, then:  \nSlant height (ℓ) =√ℎ2 +􀝎2  \nArea of curved surface = 􀟨rℓ = 􀟨r√ℎ2 +􀝎2  \nTotal surface area = Area of curved surface + Area of base = 􀟨rℓ + 􀟨􀝎 2 = 􀟨r(ℓ + r)  \n8. If r is the radius of a sphere, then: Surface area = 􀟨􀝎 2  \nVolume = 43 􀟨􀝎 3  \nVolume = 13 􀟨􀝎 2 ℎ  \n9. If r is the radius of a hemisphere, then: Area of curved surface = 2􀟨􀝎2  \nTotal surface Area = Area of curved surface + Area of base  \n= 2􀟨􀝎2 +􀟨􀝎2 = 3􀟨􀝎2 2  \nVolume = 􀟨􀝎 3  \n3  \nSurface Area of Combined Figures  \nAreas of complex figures can be broken down and analysed as simpler known shapes. By finding the areas of these known shapes, we can find out the required area of the unknown figure.  \nExample: 2 cubes each of volume 64 cm 3 are joined end to end. Find the surface area of the resulting cuboid.  \nLength of each cube = 64(1/3","cbCaieLopBroLXX9","https://ap.wps.com/l/cbCaieLopBroLXX9","pdf",1750695,31,"English","# Chapter 13: Surface Areas and Volumes\n## Surface area and volume definitions\n## Cuboid and cube formulas\n## Cylinder formulas\n## Right circular hollow cylinder formulas\n## Cone, sphere, and hemisphere formulas\n## Surface area and volume of combined figures\n## Frustum of a cone formulas","[{\"question\":\"What is the difference between surface area and volume for a solid?\",\"answer\":\"Surface area is the sum of the areas of all faces of a solid. Volume is the space occupied by the solid object.\"},{\"question\":\"How do you calculate the total surface area and lateral surface area of a cuboid?\",\"answer\":\"For a cuboid with length l, breadth b, height h, TSA = 2(lb + bh + hl) and LSA = 2h(l + b), which excludes the top and bottom faces.\"},{\"question\":\"What formulas are used for the surface area and volume of a cylinder?\",\"answer\":\"For radius r and height h, CSA = 2πrh and TSA = 2πrh + 2πr² = 2πr(h + r). Volume is V = πr²h.\"}]","Chapter 13 - Surface Areas and Volumes - Surfaces, TSA/LSA, Cylinder/Cone/Sphere, Combined Figures | PDF",78]