[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297318-105":59,"doc-detail-297318-en":123},{"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":116,"head_meta":118,"extra_data":120,"updated_unix":122},105,"en","geometry-12th-grade-surface-area-and-volume","Geometry - 12th Grade Surface Area and Volume","","Geometry chapter notes covering surface area and volume of key 3D solids. Topics include naming prisms by base shape, identifying right versus oblique prisms, computing lateral and total surface area, and counting lateral edges and faces. It also reviews pyramids (including regular pyramids) with slant height, lateral area, and total area. Additional sections address circular solids—cylinders, cones, and spheres—followed by volume formulas and example problems for prisms, pyramids, cones, and spheres.",{"@graph":69,"@context":115},[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":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/geometry-12th-grade-surface-area-and-volume/297318/",{"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-12th-grade-surface-area-and-volume/297318.png","ImageObject",300,407,{"name":92,"@type":93},"WPS_1786070896","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"Which circular solids are included and how are their lateral and total surface areas defined?","Question",{"text":113,"@type":114},"The notes cover cylinders, cones, and spheres. They provide lateral area formulas (cylinder, cone) and a total surface area formula for cylinder and cone, plus sphere total area as 4πr² (no separate base).","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},297318,1789743793,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":122,"read_time":136,"preview_page_count":4},549768072016,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Geometry,12.1:Surface area of prisms  \n   \nSolid shapes with flat faces are calledThe surfaces are called faespelygbnpolyhedra  \nand each is aThe lines where the faces intersect are called dge S  \nPrisms have:  \n·2 congruent,parallel faces called bases.  \n·parallel edges that connect corresponding vertices of the 2 parallel faces called lateraledges.  \nhas-eedgefacelapAehase  \nThe faces that are not bases are called lateral faces.  \n# Naming prisms:\n\n● Named by the shape of the bases.  \n·Right if lateral edges are perpendicular to bases,oblique if not perpendicular  \nbase  \nighiaularim  \nri+szuave pisn  \nrisht pentasonal pnSh.  \noqueanosm  \nbliqge heagoal prsm  \nmof、  \nLateral Surface Area-the sum of the areas of the lateral faces.  \n   \nall faces,  \n   \nTotal Surface Area-the sum of the areas of the lateral faces plus the areas of the  \neS.  \nExample:=12=81  1)s.A=550+21902^212可(b)L3.A=67+187+1272ssou? )rgntamAbah=84二 2√Y√i5 =45=√245=√4 o=26e=Ji(642)(c)Tis.A=316+8√厂s uzA=12(14126Y(12-(2)10)bLSA、=84/12+12=316u²(a) hish+ thangabeA=10i=(12D3A₄=1eres-me4=84=⑫4=b1y中84  \n   \n(a)Name the prism.(b)Find lateral surface area.(c)Find total surface area.(d)How many lateral edges?(e)How many lateral faces?Practice:  \n(a)Name the prism.(b)Find lateral surface area.(c)Find total surface area.  \nPractice:l=18,w=9,h=9  \n(a)Name the prism.  \n(b)Find lateral surface area.  \n(c)Find total surface area.  \n公  \n(bLSA=1648u  \nSolid shapes with 2 congruent bases are called prismsSolid shapes with only 1 base are calledramids  \nPyramids have:  \n●1 base.  \n·Lateral edges which meet at a point calledthe vertex,  \nprism  \nA pyramid is a regular pyramid if:  \n··The base is a regular polygon.  \n·The lateral edges are congruent.  \nTherefore,the lateral faces of a regular pyramid areisosceles triangles.  \npamldresulhe  \n rramid rreg  \nA quick review..ldentify the slant height and altitude:  \nldentify the lateral edge and altitude:  \nalti+wbesbnt heigh+  \ną)+Hudeateraledge  \nrish+tnanle  \nWhat kinds of triangles are determined from the sides above?  \n=14Yu  \nPractice:For the regular,square pyramid:(a)Find the area of each lateral face  \n(b)Find the pyramid's lateral area.  \n(c)Find the pyramids total area.  \nPractice:For the regular,triangular pyramid:  \nt=1bh=1(16)=1(15)=120  \n③  \nA1(6=36+  \nPractice:HW\\#7.A regular pyramid has a slant height of 12 and lateral edge of 15What is...  \n(a)...the perimeter of the base?  \n(b)..the pyramid's lateral area?  \n(c).….the area of the base?  \nx4218,2199÷3  \n(d).….the pyramid's total area?  \n132u²(a)La)1Y,4y=22  \n10幼Ab,=  \nGeometry,12.3:Surface area of circular solids  \n   \n3 solids that include circles:  \ninde  \nspere  \nCone  \nLateral Area:L.A.ylinder=C·h=2πrh  \nnone  \n   \n(no lateral edges)  \nT.A.cyinder=L.A.+2Abase  \nT.A.cone=L.A.+Abase  \nT.Asphere=4πr²=πrl+πr²=2πrh+2  \nTotal Area:  \nExamples/Practice:Find the lateral area and the total area.  \n536T=YT.9=Yπ3²T.A,=4πr²LA.(none)  \nFind total surface area:  \nA=b.h  \nrecangle  \nA=10,2= Zo  \nY(0π)=357二207+507=7071TiAcyi, = 2en+2(m²)=207+2(πs²)LA. 2Tch=2π5.2=207  \n# Geometry,12.4:Volumes of Prisms and Cylinders\n\nTry these..Find the volume.  \nTry these...  \nFind the volume of the triangular prism:  \n3 The area of the shaded face of the rightpentagonal prism is 51.Find the prism'svolume.  \nrchTry these:12  \nFind the volume of cement needed to form the concrete pedestal shown:  \n# Geometry,12.5:Volumes of Pyramids and Cones\n\n签  \nCompare this pyramid and rectangular prism with same base:  \nExamples:二104=You3=3(30)4)o be ocercenerpexdoesnsthaye  \nB=12  \nbase area=702=B  \nV=÷Bh=专(12)(4)  \nRh  \nv=L6u³  \nTry these.Find the volume...  \n=7213  \n二许  \n10二  \n(height =12)  \n≠490√ 3  \noeVolume of a cone:fa cena isa cick(B=πr2)  \nVeyl,≥Bh  \n一9TT S0=YS07  \nB=mr²=²=777  \n二价=T732Bπr  \n>37πT Y  \n12T7  \n(≈1951,ym³)m早950T7 4277Vi+a =Vcyi+V20e  \n# Geometry,12.6:Volumes of Spheres\n\n   \n# Volume of a sphere:\n\nExamples:  \nFind the volume o  \n8.A hemispherical dome has a height of 30 m.  \n(a)Find the","cbCaiovRMiypJAGh","https://ap.wps.com/l/cbCaiovRMiypJAGh","pdf",624825,"English","# Naming prisms\n## Lateral and total surface area\n# Pyramids\n## Slant height, altitude, lateral area\n# Surface area of circular solids\n## Cylinder, cone, sphere\n# Volumes of prisms and cylinders\n# Volumes of pyramids and cones\n# Volumes of spheres","[{\"question\":\"Which circular solids are included and how are their lateral and total surface areas defined?\",\"answer\":\"The notes cover cylinders, cones, and spheres. They provide lateral area formulas (cylinder, cone) and a total surface area formula for cylinder and cone, plus sphere total area as 4πr² (no separate base).\"}]","Geometry - 12th Grade Surface Area and Volume | PDF",23]