[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297391-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297391-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","3d-geometry-formulas","3D-Geometry-Formulas","","3D-Geometry-Formulas provides a compact set of solid-geometry calculations for common shapes, focusing on core measures such as surface area and enclosed volume. It includes formulas for cubes, cuboids, cones, cylinders, spheres, pyramids, ellipsoids, and prisms, along with supporting quantities like face diagonals, space diagonals, slant height, lateral surface area, circumferences, and edge/perimeter totals. Variables and geometric parameters (e.g., radius, height, dimensions, coordinates) are listed to support direct substitution.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/3d-geometry-formulas/297391/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/3d-geometry-formulas/297391.png","ImageObject",300,407,{"name":42,"@type":43},"Maeve","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",18,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What does the cube surface area formula represent?","Question",{"text":63,"@type":64},"It gives the total area of all six faces of the cube. The formula uses the cube’s side length through the standard surface-area relationship.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is the cube space diagonal determined?",{"text":68,"@type":64},"The cube space diagonal is found using a three-dimensional extension of the Pythagorean theorem. It relates the diagonal to the cube’s side length.",{"name":70,"@type":61,"acceptedAnswer":71},"What elements are included in cone surface area calculations?",{"text":72,"@type":64},"Cone surface area is broken into base area and lateral surface area, with their sum forming the total surface area. The slant height is used for the lateral part.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},297391,1789744209,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":124,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144},5909877438554,"https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272","3DGeometry Formulas  \nSurfac Area Formulas  \nVolume Formulas  \nCube Formulas  \n( s = side length of the cube )  \nSurface Area  \nThe surface area ( A ) of a cube is the total area of all six faces.  \nVolume  \nThe volume ( V ) of a cube is the amount of space enclosed within the cube.  \nDiagonal of a Face  \nThe diagonal (d_f) of any face of the cube can be found using the Pythagorean theorem.  \nSpace Diagonal  \nThe space diagonal (d_s ) of the cube, it can be found using the threedimensional Pythagorean theorem.  \nPerimeter of One Face  \nThe perimeter ( P_f) of one face of the cube is the sum of the lengths of the four edges forming that face.  \nTotal Edge Length  \nThe total edge length ( E ) of a cube is the sum of the lengths o f all twelve edges.  \nCuboid Formulas  \nSurface Area  \nLength (l)  Width (w )  Height (h)  \nThe surface area is the totalarea of all six faces of the cuboid.  \nVolume  \nThe volume of a cuboid is the amount of space it occupies.  \nDiagonal Length  \nThe diagonal of a cuboid stretches from one vertex to the opposite vertex through the interior of the cuboid.  \nFace Diagonals  \n Face Diagonal on Length and Width ( Front/Back Face)  \nFace Diagonal on Length and Width ( Front/Back Face)  \nFace Diagonal on Length and Width ( Front/Back Face)  \nCuboid Formulas  \nPerimeter of Edges  \nThe total perimeter of all the edges of a cuboid.  \nLateral Surface Area  \nThe lateral surface area of a  cuboid is the sum of the areas of the four vertical faces.  \nCone Formulas  \nVolume of aCone  \nThe volume V of a cone can the following formula:  \n r is the radius of the base  \nbe calculated  \nusing  \n h is the height of the cone  \nSurface Area  \na. Base Area  \nb. Lateral Surface Area  \nc. Total Surface Area  \nTotal Edge Length  \nThe slant height l is the distance from the base to the apex along the surface of the cone.  \nCylinder Formulas  \nSurface Area  \nh  \n V is the volume  \n r is the radius of the base  h is the height  \nVolume  \nLateral Surface Area ( Curved Surface Area)  \nArea of the Circular Bases  \nTotal Surface Area Calculation  \nSphere Formulas  \nSurface Area  \n r = Radius of the sphere  \n π ( Pi) = Approximately 3.14159  \n( A = Surface Area)  \nVolume  \n( V = Volume)  \nLateral Surface Area ( Curved Surface Area)  \nC = Circumference of the great circle  \nArea of the Circular Bases  \n(x, y, z ) = Coordinates of any point on the surface of the sphere  \n (h, k, l) = Coordinates of the center of the sphere  \nPyrmid Formulas  \nSurface Area  \nr = Radius of the sphere  \n π ( Pi) = Approximately 3.14159  \nSquare Base Rectangular Base Triangular Base  \nVolume  \nLateral surface area ( regular pyramid)  \nSlant height ( square base and rectangular base )  \nPerimeter ( square base, rectangular base & triangular base)  \nSquare Base Rectangular Base Triangular Base  \nEllipsoid Formulas  \nSurface Area  \nVolume  \nEccentricity of an Ellipsoid  \nSlant height ( square base and rectangular base )  \nPerimeter ( square base, rectangular base & triangular base)  \nPrism Formulas  \nVolume  \nB is the area of the base  \n P is the perimeter of the base  h is the height of the prism  \nThe volume 􁭯 of a prism  \nSurface Area  \nThe surface area 􁭬􁭚 of a prism  \nLateral Surface Area of a Prism  \nThe lateral surface area 􁭥􁭬􁭚  \nBase Area Formulas for Specific Prisms Rectangular Prism  \nB is Area of the base  \n P is Perimeter of the base  l is the length  \n w is the width  \nTriangular Prism  \nP is Perimeter of the base  \n bb is the base length of the triangle  h is the height of the trianglew is the  \nwidth  \n a, b, and c are the side lengths of the  \ntriangle  \nCylinder ( as a Circular Prism)  \nB is the Area of the base  \n r is the radius of the base  \n P is the Perimeter of the base","cbCaivdBpePDs5z1","https://ap.wps.com/l/cbCaivdBpePDs5z1","pdf",760608,"English","# Cube Formulas\n## Surface Area\n## Volume\n## Diagonals and Perimeters\n# Cuboid Formulas\n## Surface Area and Volume\n## Diagonal and Edge Measures\n# Cone Formulas\n## Volume\n## Surface Area (Base, Lateral, Total)\n## Slant Height\n# Cylinder Formulas\n## Surface Area\n## Lateral and Base Areas\n## Total Surface Area\n# Sphere Formulas\n## Surface Area and Volume\n## Coordinates and Great Circle Measures\n# Pyramid Formulas\n## Surface Area\n## Volume\n## Slant Height and Perimeters\n# Ellipsoid Formulas\n## Surface Area and Volume\n## Eccentricity and Related Measures\n# Prism Formulas\n## Volume and Surface Area\n## Lateral Surface Area\n## Base Formulas for Specific Prisms","[{\"question\":\"What does the cube surface area formula represent?\",\"answer\":\"It gives the total area of all six faces of the cube. The formula uses the cube’s side length through the standard surface-area relationship.\"},{\"question\":\"How is the cube space diagonal determined?\",\"answer\":\"The cube space diagonal is found using a three-dimensional extension of the Pythagorean theorem. It relates the diagonal to the cube’s side length.\"},{\"question\":\"What elements are included in cone surface area calculations?\",\"answer\":\"Cone surface area is broken into base area and lateral surface area, with their sum forming the total surface area. The slant height is used for the lateral part.\"}]","3D-Geometry-Formulas | PDF",25]