[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297261-105":59,"doc-detail-297261-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-cube-solid-geometry-basics","Surface Area and Volume - Cube - Solid geometry basics","","Surface Area and Volume explains how to work with three-dimensional solids using key definitions and measurements. It covers total surface area, volume, lateral surface area, and curved surface area, then introduces prisms, including right prisms and their lateral faces. It derives formulae for cuboids and cubes, and applies them to real problems such as finding room diagonals and calculating costs of flooring and whitewashing. Worked examples reinforce dimension-finding and volume computations for composite cuboids.",{"@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-cube-solid-geometry-basics/297261/",{"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-cube-solid-geometry-basics/297261.png","ImageObject",300,407,{"name":92,"@type":93},"Maeve","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",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are total surface area and volume of a solid?","Question",{"text":113,"@type":114},"Total surface area is the total area enclosed by all the bounding surfaces of the solid, measured in square units. Volume is the amount of space enclosed by the bounding surface(s), measured in cubic units.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you determine lateral surface area and curved surface area?",{"text":118,"@type":114},"Lateral surface area is the area of all surfaces excluding the base and top (if present). Curved surface area is the total area of all curved surfaces of the object.",{"name":120,"@type":111,"acceptedAnswer":121},"What formulas are used for a cube and a cuboid?",{"text":122,"@type":114},"For a cube with edge a: lateral surface area is 4a², total surface area is 6a², and volume is a³. For a cuboid with length l, breadth b, height h: lateral surface area is 2(l+b)h, total surface area is 2(lb+bh+lh), and volume is lbh.","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},297261,1789743410,{"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":24,"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},5909877438554,"https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272","SURFACE AREA AND VOLUME  \n• Surface Area of Cube  \n• Volume of Cube  \n• Surface Area of Cuboid  \n• Volume of Cuboid  \nIntroduction  \nYou can draw some shapes on your notebook and blackboard completely. These are called plane figures or twodimensional figures. We know what rectangles, squares , and circles are, what we mean by their perimeters and areas, and how we can find them. It would be interesting to see what happens if we cut out many of these plane figures of the same shape and size from cardboard sheets and stack them up in a vertical pile. Through this process, we shall obtain some solid figures such as a prism, a cuboid, a cylinder, etc.  \nSurface Area and Volume  \nAny object which is occupying space is called a solid. The total area enclosed by all the bounding surfaces of the solid is called the total surface area of the solid. It is measured in square units. Also , the amount of space enclosed by the bounding surface or surfaces of a solid is called the volume of the solid. It is measured in cubic units.  \nLateral surface area  \nThe lateral surface area of an object is the area of all the surfaces of the object, excluding its base and top (if there are any) . The lateral surface area is the area of the lateral surface.  \nCurved surface area  \nThe total area of all the curved surfaces in the object is the curved surface area.  \nPrism  \nA prism is a solid with identical ends, flat surfaces, and the same cross-sectional area all along its length. The top and the bottom surfaces are two congruent and parallel polygons(base) . The lateral faces are parallelograms.  \nThe line joining the centres of the top and the bottom parallel polygons is called the height or axis of the prism. If two parallel and congruent polygons are regular and, if the axis is perpendicular  \nto the base, then the prism is called a right prism. The lateral surfaces of a right prism are rectangles. Notes: The following points hold good for all prisms.  \n1. The number of lateral faces = The number of sides of the base.  \n2. The number of edges of a prism = The number of sides of the base × 3.  \n3. The sum of the lengths of the edges = 2(The perimeter of the base) + The number of sides × Height.  \n4. For a prism, whose base is a polygon, the Number of vertices + the Number of faces = Number of edges + 2. This is known as Euler’s formula, i.e., V + F = E + 2.  \nPrism  \nSurface Area and Volume of a Cube and a Cuboid  \nCuboid  \nIn a right prism if the base is a rectangle, then the right prism is called a cuboid. There are 3 dimensions in all solids and so does the cuboid,  \nthe three dimensions of the cuboid are its length (l), breadth (b) and height(h) .  \n1. The lateral surface area of a cuboid = 2(l + b)h sq. units,  \n2. The total surface area of a cuboid = LSA + 2(Base area) = 2(l + b)h + 2lb = 2(lb + bh + lh) sq. units.  \n3. The volume of a cuboid = (lb)h = lbh cubic units, 4. Diagonal of a cuboid = √l2 + b 2 + h2 units.  \nCube  \nIn a cuboid, if its length, breadth and height are equal, then it is called a cube. All the edges of a cube are equal. Thus, the edge in itself is completely sufficient to determine the size of the cube.  \nIf the edge of a cube is ‘a’ units, then  \n1. The lateral surface area of the cube = 4a2.  \n2. The total surface area of the cube = LSA + 2(Area of base) = 4a2 + 2a2 = 6a2 units.  \n3. The volume of the cube = a3.     \n4. The diagonal of the cube = √a2 + a2 + a2 = √3a2 units.  \nExample:  \nThe dimensions l × b × h of a room are 12 m × 7 m × 5 m. Find:  \n(a) The diagonal of the room.  \n(b) The cost of flooring at the rate of Rs 2 per m2.  \n(c) The cost of white washing the inside of the room excluding the floor at the rate of Rs  3 per m2. Solution: (a)The diagonal of the room = √l2 + b 2 + h2 = √122 + 72 + 52 = √144 + 49 + 25 = √218 m.  \n(b)To find the cost of flooring, we should know the area of the base.  \nBase area = l x b = 12 × 7 = 84 m2 . ∴ Cost of flooring = 84 × 2 = Rs 168.  \n(c)Total area to be whitewashed  \n= LS","cbCaiqsuZTPlXLF9","https://ap.wps.com/l/cbCaiqsuZTPlXLF9","pdf",804293,"English","# Introduction\n# Surface Area and Volume\n## Lateral surface area\n## Curved surface area\n# Prism\n# Surface Area and Volume of a Cube and a Cuboid\n## Cuboid\n## Cube\n# Examples and Practice Problems","[{\"question\":\"What are total surface area and volume of a solid?\",\"answer\":\"Total surface area is the total area enclosed by all the bounding surfaces of the solid, measured in square units. Volume is the amount of space enclosed by the bounding surface(s), measured in cubic units.\"},{\"question\":\"How do you determine lateral surface area and curved surface area?\",\"answer\":\"Lateral surface area is the area of all surfaces excluding the base and top (if present). Curved surface area is the total area of all curved surfaces of the object.\"},{\"question\":\"What formulas are used for a cube and a cuboid?\",\"answer\":\"For a cube with edge a: lateral surface area is 4a², total surface area is 6a², and volume is a³. For a cuboid with length l, breadth b, height h: lateral surface area is 2(l+b)h, total surface area is 2(lb+bh+lh), and volume is lbh.\"}]","Surface Area and Volume - Cube - Solid geometry basics | PDF",13]