[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297453-105":59,"doc-detail-297453-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-area-related-to-circles-probability-boards","Surface Area - Area Related to Circles - Probability Boards","","The material presents formula-based study notes connecting surface area and volume concepts with common three-dimensional shapes. It summarizes key expressions for cuboid and cube, different types of cylinders (closed, open, and hollow/pipes), cone and frustum, sphere and hemisphere, and spherical shells. Tables emphasize how to compute areas using parameters such as length, breadth, height, radius, and slant height, supporting exam revision with structured relationships and definitions.",{"@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-area-related-to-circles-probability-boards/297453/",{"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-area-related-to-circles-probability-boards/297453.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the general relationship between surface area and volume in these notes?","Question",{"text":113,"@type":114},"The notes compile separate formula sets: one for calculating surface area (including curved and total surface area) and another for volume, using the shape-specific dimensions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do the notes distinguish between a closed and an open cylinder?",{"text":118,"@type":114},"For a closed cylinder, both the top and bottom face areas are included in total area, while for an open cylinder the top face is excluded, leaving only the curved area plus the base area.",{"name":120,"@type":111,"acceptedAnswer":121},"Which parameters are repeatedly used across different shapes?",{"text":122,"@type":114},"The notes repeatedly use dimensions like length, breadth, and height for cuboids/cubes, and radius and height (and slant height for cones/frustums) for circular shapes.","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},297453,1789744710,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Surface Area +Area Related toCircles +Probability Boards  \nSpecial classAtharva Puranik·Mar 31,2021  \nAce your Final examswith Unacademy Plus!  \n# Unacademy Subscriptionat FLAT 10%OFF!\n\n●●●●●●●● ●●●●●●●●  \n△  \n0  \nSurface Area&Volume  \n9  \n0  \n.  \nSurface,Area and volume  \nTable for Surface Ara G Volvme  \n\n| 8edid   |  | Lzlwed 0  \u003Cbr>8layu Au   | 0ew n②   | Jetal dua  \u003Cbr>[i+2]   | Vduwe   | Ruanu   |\n| --- | --- | --- | --- | --- | --- | --- |\n| Cuboid   |  | Also knoun as   \u003Cbr>lateral surfac   \u003Cbr>area  \u003Cbr>-2(0h+bh)   | Area of:  \u003Cbr>Top fuce=1b  \u003Cbr>Bottom face=1b  \u003Cbr>∴b+1b=21b   | 2(b+bh+h)   | L.bh   | 1:length  \u003Cbr>b:breadth  \u003Cbr>h:height   |\n| Cube   |  | Lateralsrface  \u003Cbr>area-402   | Area of.  \u003Cbr>Top face=a²  \u003Cbr>Bottom face=a²  \u003Cbr>∴a²+a²=2a²   | 4a²+20²=6²   | a   | a:Side of cube   |\n| Right circu-  \u003Cbr>lar cylinder  \u003Cbr>closed at top   |  | Curved surfac   \u003Cbr>ar=2mh   | Area of  \u003Cbr>Topfae=πr²  \u003Cbr>Bottomt face=πr  \u003Cbr>∴m²+m²=2m²   | 2m²+2mh  \u003Cbr>Or,  \u003Cbr>2m(r+h)   | m²h   | r:radius  \u003Cbr>h:height ofcylinder   |\n| Right circu-  \u003Cbr>lar cylinder  \u003Cbr>open at top   |  | Curved surfac   \u003Cbr>ar=2mh   | Area of:  \u003Cbr>Top face=0  \u003Cbr>Bottom face=m²  \u003Cbr>∴0+m²=m²   | 2mh+m²  \u003Cbr>Or,  \u003Cbr>π(2h+r)   | m²h   | r:nudius  \u003Cbr>h:height of cylinder   |\n| Hollow  \u003Cbr>cylinder  \u003Cbr>(Pipe)   |  | 2πRh  \u003Cbr>·External sur.|  \u003Cbr>fae am=2πRh  \u003Cbr>·Interual sur-  \u003Cbr>fce are=2mh   | Area of  \u003Cbr>Top fuce  \u003Cbr>m{R²-r)  \u003Cbr>Bottom fuα  \u003Cbr>=mR²-r)   | 2πRh+2mh  \u003Cbr>2π(R²-r)   | +|πRh   \u003Cbr>m²h  \u003Cbr>(Externa  \u003Cbr>Ve  \u003Cbr>Internal  \u003Cbr>Vol)   | -R:Radius of ouler base  \u003Cbr>r:radius of inner base  \u003Cbr>l|h=height   |\n| Cone   |  |  | Aren of  \u003Cbr>Bottom Fac=m²   | m²+ml  \u003Cbr>Or,m(r+1)   | 号m²   | h=height of cone  \u003Cbr>r=radius of cone  \u003Cbr>1=slant height  \u003Cbr>“√²+r²   |\n| Frustum*   |  | π(R+n)   | Area of.  \u003Cbr>Top Face=m²  \u003Cbr>Bottom Face=nR²   | m²+πR2  \u003Cbr>+n(R+r)   | 3m.  \u003Cbr>R²+r²  \u003Cbr>+Rr)   | h=height offrustum  \u003Cbr>r=radius of top fuce  \u003Cbr>R=Radius ofbase  \u003Cbr>1=slant height   |\n| Sphere   |  | 4m²   | None   | 4m²   | 号m³   | r:radius ofsphere   |\n| Hemnisphere   |  |  | m²   | 3m²   | 号m³   | r:radius of  \u003Cbr>hemisphere   |\n| Spherical  \u003Cbr>shell   |  | 4πR²(Outer)  \u003Cbr>4m²(nne)   | None   | 4πR²+4m²   | 二   | R:Radius ofouter shel  \u003Cbr>r:Radius of inner shell   |\n\nN²n  \nl  \n(*Fkustum has bum dultd 2021 gxam ⑧ylabu)  \n# CSA\n\nTSA  \n# Cuboid\n\nCSA=2(L+B)*HTSA=2(LB+BH+HL)Volume=LBH  \nCubeCSA=4L²TSA=6L²Volume=L  \nCtbeind(YCSA=2πrh  \nTSA=2πr(h+r!Kxh升2íVolume =πr²h+  \nh十n12N(n+v)  \nCone  \nCSA =πrlTSA=πr(l+r)  \nVolume =1/3(πr²h)I2=√r2+h2","cbCaiidg6Q1bDSIx","https://ap.wps.com/l/cbCaiidg6Q1bDSIx","pdf",10411129,87,"English","# Surface Area & Volume\n## Surface, Area and volume\n## Formulas for 3D shapes\n### Cuboid and Cube\n### Cylinders (closed, open, hollow/pipes)\n### Cone and Frustum\n### Sphere and Hemisphere\n### Spherical shell","[{\"question\":\"What is the general relationship between surface area and volume in these notes?\",\"answer\":\"The notes compile separate formula sets: one for calculating surface area (including curved and total surface area) and another for volume, using the shape-specific dimensions.\"},{\"question\":\"How do the notes distinguish between a closed and an open cylinder?\",\"answer\":\"For a closed cylinder, both the top and bottom face areas are included in total area, while for an open cylinder the top face is excluded, leaving only the curved area plus the base area.\"},{\"question\":\"Which parameters are repeatedly used across different shapes?\",\"answer\":\"The notes repeatedly use dimensions like length, breadth, and height for cuboids/cubes, and radius and height (and slant height for cones/frustums) for circular shapes.\"}]","Surface Area - Area Related to Circles - Probability Boards | PDF",219]