[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-635143-105":59,"doc-detail-635143-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","geometry-quick-guide-5-3d-shape-formulas","GEOMETRY QUICK GUIDE 5 - 3D SHAPE FORMULAS","","Geometry Quick Guide 5 provides a compact reference for 3D shapes, explaining how all solids are described using faces, edges, and vertices. It lists volume and surface-area formulas for common solids including cubes, cuboids (rectangular prisms), pyramids, prisms, spheres, right cylinders, and right circular cones. Variables are defined for side lengths, dimensions, base area, height, and base perimeter to support direct substitution in calculations.",{"@graph":69,"@context":122},[70,84,105],{"@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/geometry-quick-guide-5-3d-shape-formulas/635143/",{"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/geometry-quick-guide-5-3d-shape-formulas/635143.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How are 3D shapes described in this guide?","Question",{"text":112,"@type":113},"All 3D shapes are described using faces, edges, and vertices. A face is a flat or curved surface, an edge is where two faces meet, and a vertex is where three or more edges meet.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What formulas are given for cubes and cuboids?",{"text":117,"@type":113},"For a cube, Volume = s^3 and Surface area = 6s^2. For a cuboid (rectangular prism), Volume = ℓ × w × h and Surface area = 2ℓh + 2ℓw + 2wh, with ℓ = length, w = width, and h = height.",{"name":119,"@type":110,"acceptedAnswer":120},"Which solids and surface-area/volume formulas are included besides cubes and cuboids?",{"text":121,"@type":113},"The guide includes pyramids (general pyramid, regular tetrahedron, and right square pyramid), prisms (general and triangular prism), and also spheres, right cylinders, and right circular cones with their respective volume and surface-area formulas.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},635143,1793008018,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","GEOMETRY QUICK GUIDE 5: 3D SHAPE FORMULAS  \n\n| 3D SHAPES\u003Cbr>All 3d shapes can be described in terms of their faces, vertices and edges.\u003Cbr>Face-a flat or curved surface Edge- line where 2 faces meet\u003Cbr>Vertex-point where 3 or more edges meet\u003Cbr>face\u003Cbr>\u003Cbr>\u003Cbr>vertex\u003Cbr>edge\u003Cbr>|  |  | CUBE\u003Cbr>Volume = s3\u003Cbr>Surface area = 6s 2\u003Cbr>where s is the length of one side |  |  | CUBOID (RECTANGULAR PRISM)\u003Cbr>Volume = ℓ x w x h\u003Cbr>Surface area = 2ℓh + 2ℓw + 2wh\u003Cbr>where ℓ = length, w = width, h = height\u003Cbr>\u003Cbr>\u003Cbr>ℓ\u003Cbr>\u003Cbr>w |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  | |  | \u003Cbr>s |  |  |  |\n| PYRAMIDS\u003Cbr>Volume of a general pyramid = 1/3 A h where A = base area and h = height |  |  | REGULAR TETRAHEDRON Volume = b 3 /6√2 Surface area = √3b 2\u003Cbr>\u003Cbr> b  |  |  | RIGHT SQUARE PYRAMID Volume = 1/3 b 2 h Surface area = b2 + 2bs |  |  |\n| |  | h |  |  |  | | | h |\n| PRISMS\u003Cbr>Volume of any prism = Ah\u003Cbr>Surface area of a closed prism = 2A + (h x p)\u003Cbr>where A = base area, h = height, p = base perimeter |  |  |  | TRIANGULAR PRISM\u003Cbr>Volume = A ℓ or ½ bhℓ\u003Cbr>Surface area = bh + 2ℓs + ℓb \u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>s\u003Cbr>b |  |  |  |  |\n| p\u003Cbr>| \u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>h |  |  |  |  |  |  |  |\n\n\n| SPHERES\u003Cbr>Volume = 4/3 пr 3\u003Cbr>Surface area = 4пr 2 | RIGHT CYLINDER\u003Cbr>Volume = пr 2 h\u003Cbr>Surface area = 2пr (r + h) |  |  | RIGHT CIRCULAR CONE Volume = 1/3 пr 2 h Surface area = пr (r + s) |\n| --- | --- | --- | --- | --- |\n| \u003Cbr>r | | | h | \u003Cbr>\u003Cbr>r\u003Cbr>h\u003Cbr>s |\n\nGEOMETRY QUICK GUIDE 5: 3D SHAPE FORMULAS  \n\n| 3D SHAPES\u003Cbr>All 3d shapes can be described in terms of their faces, vertices and edges.\u003Cbr>• Face-a flat or curved surface\u003Cbr>• Edge- line where 2 faces meet\u003Cbr>• Vertex-point where 3 or more\u003Cbr>edges meet\u003Cbr>edge \u003Cbr>\u003Cbr>\u003Cbr>face\u003Cbr> vertex\u003Cbr>|  |  |  | CUBE\u003Cbr>Volume = s3\u003Cbr>Surface area = 6s 2\u003Cbr>where s is the length of one side\u003Cbr>|  |  | CUBOID (RECTANGULAR PRISM) Volume = ℓ x w x h\u003Cbr>Surface area = 2ℓh + 2ℓw + 2wh where ℓ = length, w = width, h = height\u003Cbr>\u003Cbr>\u003Cbr>ℓ\u003Cbr>\u003Cbr>w |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| PYRAMIDS\u003Cbr>Volume of a general pyramid = 1/3 A h where A = base area and h = height |  |  |  | REGULAR TETRAHEDRON Volume = b 3 /6√2 Surface area = √3b 2\u003Cbr>\u003Cbr> b  |  |  | RIGHT SQUARE PYRAMID Volume = 1/3 b 2 h Surface area = b2 + 2bs |  |  |\n| |  |  | h |  |  |  | | | h |\n| PRISMS\u003Cbr>Volume of any prism = Ah\u003Cbr>Surface area of a closed prism = 2A + (h x p) where A = base area, h = height, p = base perimeter |  |  |  |  |  | TRIANGULAR PRISM Volume = A ℓ or ½ bhℓ\u003Cbr>Surface area = bh + 2ℓs + ℓb \u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>s\u003Cbr>b |  |  |  |\n| \u003Cbr>| \u003Cbr>h | |  |  | \u003Cbr>h |  |  |  |  |\n\n\n| SPHERES\u003Cbr>Volume = 4/3 пr 3\u003Cbr>Surface area = 4пr 2 | RIGHT CYLINDER\u003Cbr>Volume = пr 2 h\u003Cbr>Surface area = 2пr (r + h) |  |  | RIGHT CIRCULAR CONE Volume = 1/3 пr 2 h Surface area = пr (r + s) |\n| --- | --- | --- | --- | --- |\n| \u003Cbr>\u003Cbr>r | | | h | \u003Cbr>\u003Cbr>r\u003Cbr>h\u003Cbr>s |","cbCaids2Se2VXYIU","https://ap.wps.com/l/cbCaids2Se2VXYIU","pdf",248405,"English","# 3D Shapes Basics\n## Faces, Edges, Vertices\n# Solids and Formulas\n## Cube and Cuboid\n## Pyramids\n## Prisms\n## Spheres, Cylinders, Cones","[{\"question\":\"How are 3D shapes described in this guide?\",\"answer\":\"All 3D shapes are described using faces, edges, and vertices. A face is a flat or curved surface, an edge is where two faces meet, and a vertex is where three or more edges meet.\"},{\"question\":\"What formulas are given for cubes and cuboids?\",\"answer\":\"For a cube, Volume = s^3 and Surface area = 6s^2. For a cuboid (rectangular prism), Volume = ℓ × w × h and Surface area = 2ℓh + 2ℓw + 2wh, with ℓ = length, w = width, and h = height.\"},{\"question\":\"Which solids and surface-area/volume formulas are included besides cubes and cuboids?\",\"answer\":\"The guide includes pyramids (general pyramid, regular tetrahedron, and right square pyramid), prisms (general and triangular prism), and also spheres, right cylinders, and right circular cones with their respective volume and surface-area formulas.\"}]","GEOMETRY QUICK GUIDE 5 - 3D SHAPE FORMULAS | PDF",1792675384]