[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297576-105":59,"doc-detail-297576-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","3d-shapes-formulae-surface-area-and-volume","3D Shapes Formulae - Surface Area and Volume","","Covers key GCSE-style relationships for 3D shapes, focusing on calculating surface area and volume from given dimensions. Uses cross-section reasoning to derive volume as cross sectional area multiplied by depth. Includes guidance on handling shapes placed on top of others by accounting for what is not exposed. Mentions using Pythagoras for missing lengths and 3D trigonometry for pyramids when dimensions are not directly provided.",{"@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/3d-shapes-formulae-surface-area-and-volume/297576/",{"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/3d-shapes-formulae-surface-area-and-volume/297576.png","ImageObject",300,407,{"name":92,"@type":93},"Sarah ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you calculate volume using the cross-section method?","Question",{"text":112,"@type":113},"Find the area of the cross section and multiply by the depth: volume = area of cross section × depth.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"When finding surface area, what common issue must you watch for?",{"text":117,"@type":113},"For surface area, check what is not exposed, especially when one shape sits on top of another.",{"name":119,"@type":110,"acceptedAnswer":120},"What should you use if some required lengths are missing?",{"text":121,"@type":113},"Use Pythagoras to find missing lengths, and use 3D trig knowledge for pyramids when lengths are not given.","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},297576,1790855017,{"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":24,"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},962085320529,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","3D Sh pes [www.mymathscloud.com](www.mymathscloud.com) \n\n| | Surface Area – Imagine Painting The Outside Of A Shape | | | | | | | | | | | | | | | | | | | | | | | | | | | | Volume-Imaging Filling A Shape With Water | | | | | | | | | | | | | | | | | | | | | Compound Shapes-Two Shapes Combined | | | | | | |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| | Cube\u003Cbr>| | | | | | | | | | | | | | | | | | | | | | | | | | | | Imagine cutting through a shape with a knife\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>or or\u003Cbr>\u003Cbr>volume = area of cross section × depth = 5675 89 × depth\u003Cbr>| | | | | | | | | | | | | | | | | | | | | You commonly encounter a shape on top of another shape. For surface area you need to watch out for what is not exposed! | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Cone and Sphere | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Surface Area | | | | Volume | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | \u003Cbr>Cuboid\u003Cbr>opens to\u003Cbr>⟹\u003Cbr>| | | \u003Cbr>| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | \u003Cbr>Cube | Cross section\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>area of cross section × depth = area of square × depth\u003Cbr>! \"\u003Cbr>= ; ; = ; | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Cylinder and Sphere | | | | | | |\n| | | | | \u003Cbr>\u003Cbr>Note: You may need to use Pythagoras to find any missing lengths The front face could have a right angled triangle instead of equilateral | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Surface Area | | | | Volume | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | area of cross section x depth = -\\# - = -$ | | | | | | | | | | | | | | | | | | | | | | | | | |\n| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | \u003Cbr>2 | | | | | | |\n| | | | | | | | | | | | | | ","cbCaidi65Hn4kkvP","https://ap.wps.com/l/cbCaidi65Hn4kkvP","pdf",5054800,"English","# Surface Area\n## Exposed faces in composite shapes\n# Volume\n## Cross-section method: area of cross section × depth\n## Notes on missing lengths (Pythagoras)","[{\"question\":\"How do you calculate volume using the cross-section method?\",\"answer\":\"Find the area of the cross section and multiply by the depth: volume = area of cross section × depth.\"},{\"question\":\"When finding surface area, what common issue must you watch for?\",\"answer\":\"For surface area, check what is not exposed, especially when one shape sits on top of another.\"},{\"question\":\"What should you use if some required lengths are missing?\",\"answer\":\"Use Pythagoras to find missing lengths, and use 3D trig knowledge for pyramids when lengths are not given.\"}]","3D Shapes Formulae - Surface Area and Volume | PDF",1789745869]