[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297605-105":59,"doc-detail-297605-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-area-and-volume-cuboid-cube-cylinder-cone-sphere","Surface Area and Volume - Cuboid, Cube, Cylinder, Cone, Sphere","","A math learning sheet focused on surface area and volume for common 3D shapes. It defines cuboids, cubes, right circular cylinders, right circular cones, and spheres, then derives key formulas for total surface area, lateral surface area (where applicable), curved surface area, and volume. Expressions are presented using standard variables for length, breadth, height, radius, and slant height, including relations like l^2 = h^2 + r^2 and the cone volume as one-third of a cylinder with the same base and height.",{"@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-area-and-volume-cuboid-cube-cylinder-cone-sphere/297605/",{"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-area-and-volume-cuboid-cube-cylinder-cone-sphere/297605.png","ImageObject",300,407,{"name":92,"@type":93},"Mabel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the total surface area formula for a cuboid?","Question",{"text":113,"@type":114},"For a cuboid with length l, breadth b, and height h, TSA = 2(lb + bh + lh).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you find the lateral surface area of a cuboid?",{"text":118,"@type":114},"LSA for a cuboid equals 2h(l + b), using the side faces excluding the top and bottom.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the volume of a right circular cone in terms of cylinder volume?",{"text":122,"@type":114},"A right circular cone has volume equal to one-third of a cylinder with the same radius and height: V = (1/3)πr^2h.","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},297605,1789746134,{"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":29,"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},7971474920318,"https://ap-avatar.wpscdn.com/avatar/74000ee537e6b0ca360?x-image-process=image/resize,m_fixed,w_180,h_180&k=1788430171632181674","Surface Area and Volume  \nCuboid  \nCuboid is a three dimensional Shape.  \nCuboid is made from six rectangular faces, which are placed at right angles.  \nThe total surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.  \nTotal Surface Area of a Cuboid  \nConsider a cuboid whose length is l cm, breadth is b cm and height h cm. Area offace ABCD = Area of Face EFGH = (l × b)cm2  \nArea of face AEHD = Area offace BFGC = (b × h)cm2  \nArea of face ABFE = Area of face DHGC = (l × h)cm2  \nTotal surface area (TSA) of cuboid = Sum of the areas of all its six faces = 2(l × b) + 2(b × h) + 2(l × h)  \nTSA (cuboid)= 2(lb + bh +lh)  \nLateral Surface Area of a Cuboid  \nLateral surface area (LSA) is the area of all the sides apart from the top and bottom faces. Lateral surface area of the cuboid  \n= Area of face AEHD + Area offace BFGC + Area of face ABFE + Area of face DHGC = 2(b × h) + 2(l × h)  \nLSA (cuboid) = 2h(l + b)  \nCube  \nA  whose length, breadth and height are all , is called a  . It is a threedimensional shape bounded by  . It has 12 edges and 8 vertices.  \nTotal Surface Area of a cube  \nFor cube, length = breadth = height Suppose length of an edge = a  \nTotal surface area(TSA) of the cube = 2(a × a + a × a + a × a) TSA(cube) = 2 × (3a2 ) = 6a2  \nLateral Surface area of a cube  \nLateral surface area (LSA) is the area of all the sides apart from the top and bottom faces. Lateral surface area of cube = 2(a × a + a × a) = 4a2  \nRight Circular Cylinder  \nA right circular cylinder is a closed solid that has two parallel circular bases connected by a curved surface in which the two bases are exactly over each other and the axis is at right angles to the base.  \nCurved Surface area of a right circular cylinder  \nTake a cylinder of base radius r and height h units. The curved surface of this cylinder, if  \nopened along the diameter (d = 2r) of the circular base can be transformed into a rectangle of length 2πr and height h units. Thus,  \nCurved surface area(CSA) of a cylinder of base radius r and height h = 2π × r × h  \nTotal surface area of a right circular cylinder  \nTotal surface area(TSA) of a cylinder of base radius r and height h = 2π × r × h + area of two circular bases  \n⇒ TSA = 2π × r × h + 2 × πr2 ⇒ TSA = 2πr(h + r)  \nRight Circular Cone  \nA right circular cone is a circular cone whose axis is perpendicular to its base.  \nRelation between slant height and height of a right circular cone  \nA right-circular cone.  \nThe relationship between slant height(l) and height(h) of a right circular cone is:  \nl2 = h2 + r2 (Using Pythagoras Theorem)  \nWhere r is the radius of the base of the cone.  \nCurved Surface Area of a Right Circular Cone  \nConsider a right circular cone with slant length land radius r.  \nIf a perpendicular cut is made from a point on the circumference of the base to the vertex and the cone is opened up, a sector of a circle with radius lis produced as shown in the figure below:  \nLabel A and B and corresponding b1, b2 ...bn at equal intervals, with O as the common vertex. The Curved surface area(CSA) of the cone will be the sum of areas of the small triangles : 12 × (b1 + [b2. . . bn](b2. . . bn)) × l  \n(b1 + [b2. . . bn](b2. . . bn)) is also equal to circumference of base = 2πr  \nCSA of right circular cone = 12 × (2πr) × l = πrl (On substituting the values)  \nTotal Surface Area of a Right Circular Cone  \nTotal surface area(TSA) = Curved surface area(CSA) + area of base = πrl + πr2 = πr (l + r)  \nSphere  \nA sphere is a three-dimensional figure (solid figure), which is made up of all points in the space which lie at a constant distance called the radius, from a fixed point called the center of the sphere.  \nSurface area of a Sphere  \nThe surface area of a sphere of radius r = 4 times the area of a circle of radius r = 4 × (πr2 ) For a sphere Curved surface area(CSA) = Total Surface area(TSA) = 4πr2  \nVolume of a Cuboid  \nThe volume of a cuboid is the product of its dimensions. Volume of a cuboid","cbCaiqi31t6xOE4e","https://ap.wps.com/l/cbCaiqi31t6xOE4e","pdf",187944,"English","# Surface Area and Volume\n## Cuboid\n## Cube\n## Right Circular Cylinder\n## Right Circular Cone\n## Sphere\n## Volume of Solids\n## Volume and Capacity","[{\"question\":\"What is the total surface area formula for a cuboid?\",\"answer\":\"For a cuboid with length l, breadth b, and height h, TSA = 2(lb + bh + lh).\"},{\"question\":\"How do you find the lateral surface area of a cuboid?\",\"answer\":\"LSA for a cuboid equals 2h(l + b), using the side faces excluding the top and bottom.\"},{\"question\":\"What is the volume of a right circular cone in terms of cylinder volume?\",\"answer\":\"A right circular cone has volume equal to one-third of a cylinder with the same radius and height: V = (1/3)πr^2h.\"}]","Surface Area and Volume - Cuboid, Cube, Cylinder, Cone, Sphere | PDF",15]