[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297260-105":59,"doc-detail-297260-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","surface-areas-and-volumes-basics","Surface Areas and Volumes - Basics","","Key concepts and formulas for computing surface areas and volumes of common 3D solids are presented, starting with cuboids, cubes, cylinders, right circular cones, spheres, and hemispheres. Definitions of total surface area (TSA), curved surface area (CSA), and lateral surface area (LSA) are used to derive expressions in terms of relevant dimensions. The document also covers diagonal length, volume relationships among solids, and applications to combined figures and shape conversions, including frustums and constant-volume casting.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/surface-areas-and-volumes-basics/297260/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/surface-areas-and-volumes-basics/297260.png","ImageObject",300,407,{"name":92,"@type":93},"Violet","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you calculate the total surface area of a cuboid?","Question",{"text":113,"@type":114},"Add the areas of all six rectangular faces. The derived formula is TSA = 2(lb + bh + lh).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are the curved surface area and total surface area of a cylinder?",{"text":118,"@type":114},"CSA = 2πrh. TSA = 2πrh + 2πr² = 2πr(h + r).",{"name":120,"@type":111,"acceptedAnswer":121},"How can volume be used to convert one solid shape into another?",{"text":122,"@type":114},"When a solid is melted and recast, volume remains constant. Set the original volume equal to the new solid’s volume and solve for the unknown dimension, as shown in the sphere-to-cylinder example.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},297260,1789743409,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144},4398048950312,"https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908","Surface Areas and Volumes  \nBasics  \nCuboid and It's Surface Area  \nThe surface area of a cuboid is equal to the sum of the areas of its six rectangular faces. Consider a cuboid whose dimensions are l × b × h respectively.  \nCuboid with length l, breadth b and height h  \nTotal surface area of 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. 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 = √l2 + b2 + h2  \nCube and Its Surface Area  \nFor a cube length = breadth = height  \nCube with length l  \nTSA (cube) = 2 × (3l2 ) = 6l2  \nSimilarly, the Lateral surface area of cube = 2(l × l + l × l) = 4l2 Note: Diagonal of a cube = √3l  \nCylinder and Its Surface Area  \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 + 2πr2  \n= 2πr(h + r)  \nRight Circular Cone and Its Surface Area  \nConsider a right circular cone with slant length l, radius r and height h.  \nCone with base radius r and height h  \nCSA of right circular cone = πrl  \nTSA = CSA + area of base = πrl + πr2 = πr (l + r)  \nSphere and Its Surface Area  \nFor a sphere of radius r  \nCurved Surface Area (CSA) = Total Surface Area (TSA) = 4πr2  \nSphere with radius r  \nVolume of a Cuboid  \nVolume of a cuboid = (base area) × height = (lb)h = lbh  \nVolume of a Cube  \nVolume of a cube = base area×height  \nSince all dimensions of a cube are identical, volume = l3 Where lis the length of the edge of the cube.  \nVolume of a Cylinder  \nVolume of a cylinder = Base area × its height = (π × r2 ) × h = πr2 h  \nCylinder with height h and base radius r  \nVolume of a Right Circular Cone  \nThe volume of a Right circular cone is 13 times that of a cylinder of same height and base. In other words, 3 cones make a cylinder of the same height and base.  \nVolume of a Right circular cone = 13~~ ~~ πr2 h  \nWhere r is the radius of the cone and his the height of the cone.  \nVolume of a Sphere  \nThe volume of a sphere of radius r = 43 πr3  \nHemisphere and Its Surface Area  \nHemisphere of radius r  \nWe know that the CSA of a sphere = 4πr2 . A hemisphere is half of a sphere.∴ CSA of a hemisphere of radius r = 2πr2  \nTotal Surface Area = curved surface area + area of the base circle ⇒TSA = 3πr2  \nVolume of Hemisphere  \nThe volume (V) of a hemisphere will be half of that of a sphere.∴ Volume of the hemisphere of radius r = 23~~ ~~ πr3  \nCombination of Solids  \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 cm3 are joined end to end. Find the surface area of the resulting cuboid.  \n1  \nLength of each cube = 64 3 = 4cm  \nSince these cubes are joined adjacently, they form a cuboid whose length l = 8cm. But height and breadth will remain same = 4cm.  \nCombination of 2 equal cubes  \n∴ The new surface area = TSA  \n= 2(lb + bh + lh)  \n= 2(8 × 4 + 4 × 4 + 8 × 4)  \n= 2(32 + 16 + 32)  \n= 2(80)  \n= 160 cm2  \nVolume of Combined Solids  \nThe volume of complex objects can be simplified by visualising it as a combination of shapes of known solids.  \nExample: A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius.  \nThe above figure can be visualised a","cbCaid0itMssK9Io","https://ap.wps.com/l/cbCaid0itMssK9Io","pdf",256940,"English","# Basics\n## Cuboid and Its Surface Area\n## Cube and Its Surface Area\n## Cylinder and Its Surface Area\n## Right Circular Cone and Its Surface Area\n## Sphere and Its Surface Area\n## Volume of Solids\n## Combination of Solids\n## Shape Conversion of Solids","[{\"question\":\"How do you calculate the total surface area of a cuboid?\",\"answer\":\"Add the areas of all six rectangular faces. The derived formula is TSA = 2(lb + bh + lh).\"},{\"question\":\"What are the curved surface area and total surface area of a cylinder?\",\"answer\":\"CSA = 2πrh. TSA = 2πrh + 2πr² = 2πr(h + r).\"},{\"question\":\"How can volume be used to convert one solid shape into another?\",\"answer\":\"When a solid is melted and recast, volume remains constant. Set the original volume equal to the new solid’s volume and solve for the unknown dimension, as shown in the sphere-to-cylinder example.\"}]","Surface Areas and Volumes - Basics | PDF",25]