[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-297454-en":3,"doc-seo-297454-105":31,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},297454,2336475104736,"วิน","https://ap-avatar.wpscdn.com/avatar/22000c4c5e0e5b17e70?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786591360781797222",4,"Exam","CHAPTER-13 SURFACE AREAS AND VOLUMES - Part A","Chapter 13 focuses on surface areas and volumes of common 3D shapes, presenting key formulas for cuboid, cube, right circular cylinder, right circular cone, sphere, and hemisphere (solid and hollow). It includes relationships between lateral/curved surface area and total surface area, along with symbols for dimensions such as length, breadth, height, slant height, and radius. Part A contains multiple-choice and word problems using these formulas to compare, compute, and relate volumes and surface areas under changes of dimensions.","(i)  Total surfaceArea(T.S.A)=Curved Surface Area(C.S.A)+BaseArea  \n(ii)Forplane FigureFor Curved figureLateral surfaceArea(L.S.A)curved surface area(C.S.A)  \niii)Volume of cylinder二3xvolume of coneVolume of hemisphere二2xvolume of cone  \nvolume of cone:volume of hemisphere:volume of cylinder=1:2:3  \nV₁:V₂:V₃=1:2:3  \n二  \n# CHAPTER-13SURFACE AREAS AND VOLUMES\n\n\n| KEY POINTS   |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| Figure  \u003Cbr>S.No.Name   |  | Lateral/  \u003Cbr>Curved  \u003Cbr>Surface Area   | Total  \u003Cbr>surface  \u003Cbr>Area   | Volume   | Symbols  \u003Cbr>used for   |\n| 1.       | Cuboid   | 2(1+b)×h   | 2(Ib+bh+hl)   | lbh   | 1=Length  \u003Cbr>b=breadth  \u003Cbr>h=height   |\n|  |  |  |  |  |  |\n| 2.   | Cube   | 4a²   | 6a²   | a³   | a=side   |\n| 3.   | Right  \u003Cbr>Circular  \u003Cbr>Cylinder   | 2πrh   | 2πr(h+r)   | πr²h   | h=height  \u003Cbr>r=radius  \u003Cbr>of base   |\n|  |  |  |  |  |  |\n|  |  |  |  |  |  |\n| 4.   | Right  \u003Cbr>Circular  \u003Cbr>Cone   | πrl   | πr(1+r)   |  | h=height  \u003Cbr>r=radius  \u003Cbr>of base   |\n|  |  |  |  |  |  |\n| 5.   | Sphere   | 4πr²   | 4πr²   |  | r=radius   |\n| 6.   | Hemisphere  \u003Cbr>Solid   | 2πr²   | 3πr²   |  | r=radius   |\n| 7.   | Hemisphere  \u003Cbr>hollow   | 2πr²   | 2πr²   |  | r=radius   |\n\nCHAPTER-13SURFACE AREAS AND VOLUMES  \nPART -A  \n1.   If the volume of a sphere is numerically equal to its surface area.Thenradius of sphere is.(a)   1 unit(b)  3unit(c)  2unit(d)  6unit  \nThsurface area of asolid hemisphere having radiusr.2.(b)  3πr²(a)  2πr²πr³(c)  4πr²(d)  \n3.In a cylinders,If radius is halved and height is doubled the volume willbe.  \n(a)  Same(b)  double(c)  halved(d)  four times  \n4.   Th height of a cone of diameter 10cm and slant height13cm,is(a)   12cm(b)   13cm(c)  √69 cm(d)  √194 cm  \n5.The radius of a hemispherical balloon increases from 6cm to 12cm asair is being pumped into it.The ratios of the surface areas of theballoon in the two cases is.(a)  1:4(b)  1:3(d)  2:1(c)  2:3  \n6.How many bricks will be required to constructawall 13.5m long;6m highand 22.5cm thick ifeach brick measures(27cmx12.5cmx9cm)?(a)  6000(b)  7500(c)  5000(d)  3750  \n7.The radius ofasphere is 2r,then its volume will be.(b)  4πr³(a)(c)(d)  \n8.   The radius of a sphere is 21cm.What is the surface area of thesphere?  \n(a)  12932cm²(b)  4312cm²(c)  9702cm²(d)  5544cm²  \n9.The length of the longest pole that can be put in a room of dimensions(10mx10mx5m)is(b)  16m(a)   15m(c)   12m(d)  10m  \n10.  Acopper sphere of diameter 6cm is melted and drawn into 36cm longwire of uniform circular cross-section.Then,its radius is(a)  2cm(b)  1.5cm(c)   1.2cm(d)  1cm  \n11.  The number of planks of dimension (4mx50cm ×20cm)that can bestored in a pit which is 16m long,12m wide and 4m deepis.(a)  1900(b)  1920(c)   1800(d)  1840  \n12.  If the radius of a sphere is increased by 10%then its volume will beincreased by(a)  11.1%(b)  22.1%(c)  33.1%(d)  44.1%  \n13.  Inacylinder,radius is double and height is halved,surface area will be.(a)  halved(b)  doubled(c)  Same(d)  four times  \n14.   Two cubes have their volumes in the ratio 1:27.The ratio of theirsurface area is.(a)  1:3(b)  1:8(c)  1:9(d)  1:18  \n15.  A cone is 8.4cm high and the radius of its base is 2.1cm.It is meltedand recast into a sphere.The radius of the sphere is:(a)  4.2cm(b)  2.1 cm(c)  2.4 cm(d)  1.6cm  \n16.  If the length of diagonal of a cube is 8√3 cm,then its surface areais.(a)  768 cm²(b)  512cm²(c)  384cm²(d)  192cm²  \n17.  The total surface area ofa cube is 96cm².The volume of the cube is:(a)  8cm³(b)  512cm³(c)  64cm³(d)  27 cm³  \n18.  If each side ofa cube is doubled,then its volume,(a)  Becomes Doubled(b)  Becomes 4 times(c)   becomes 6 times(d)  become 8 times  \n19.  If a sphere is inscribed in a cube,then the ratio of the volume of thecube to the volume of the sphere will be:(a)  6:π(b)  3:π(c)  2:π(d)  3:2π  \n20.  If each edge of a cube is increased by 50%,then the percentageincrease in its surface area is.(a)  50%(b)  75%(c)  100%(d)  125%  \n21.   The lateral sur","cbCaigxm61pPEaN1","https://ap.wps.com/l/cbCaigxm61pPEaN1","pdf",3481038,12,1,15,"English","en",105,"# CHAPTER-13 SURFACE AREAS AND VOLUMES\n## Key surface-area and volume formulas\n## PART - A (questions 1-30)\n## PART - B (questions 31-38+ )","[{\"question\":\"What is the relationship between total surface area, curved surface area, and base area for a curved solid?\",\"answer\":\"Total surface area equals curved surface area plus base area. For plane figures folded from a curved figure, the lateral/curved surface area is used to form the total surface area.\"},{\"question\":\"How do you compute the volume ratios when cylinder, cone, and hemisphere have related measurements?\",\"answer\":\"The document states volume of cylinder, cone, and hemisphere in the ratio form: volume of cone : volume of hemisphere : volume of cylinder = 1 : 2 : 3, and equivalently V₁:V₂:V₃ = 1:2:3.\"},{\"question\":\"If a cylinder’s radius is halved and its height is doubled, what happens to its volume?\",\"answer\":\"Radius is reduced to half, so cross-sectional area becomes one-fourth; height doubles, so overall volume becomes half of the original.\"}]","CHAPTER-13 SURFACE AREAS AND VOLUMES - Part A | PDF",1789744711,38,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":92,"head_meta":94,"extra_data":96,"updated_unix":29},"chapter-13-surface-areas-and-volumes-part-a","",{"@graph":37,"@context":91},[38,54,74],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/exam/",3,{"item":53,"name":13,"@type":44,"position":11},"https://docshare.wps.com/document/chapter-13-surface-areas-and-volumes-part-a/297454/",{"url":53,"name":13,"@type":55,"image":56,"author":61,"headline":13,"publisher":63,"fileFormat":66,"inLanguage":24,"description":14,"dateModified":67,"datePublished":68,"encodingFormat":66,"isAccessibleForFree":69,"interactionStatistic":70},"DigitalDocument",{"url":57,"@type":58,"width":59,"height":60},"https://docshare.wps.com/thumbnails/chapter-13-surface-areas-and-volumes-part-a/297454.png","ImageObject",300,407,{"name":9,"@type":62},"Person",{"url":42,"name":64,"@type":65},"DocShare","Organization","application/pdf","2026-10-26","2026-09-18",true,{"@type":71,"interactionType":72,"userInteractionCount":20},"InteractionCounter",{"@type":73},"ViewAction",{"@type":75,"mainEntity":76},"FAQPage",[77,83,87],{"name":78,"@type":79,"acceptedAnswer":80},"What is the relationship between total surface area, curved surface area, and base area for a curved solid?","Question",{"text":81,"@type":82},"Total surface area equals curved surface area plus base area. For plane figures folded from a curved figure, the lateral/curved surface area is used to form the total surface area.","Answer",{"name":84,"@type":79,"acceptedAnswer":85},"How do you compute the volume ratios when cylinder, cone, and hemisphere have related measurements?",{"text":86,"@type":82},"The document states volume of cylinder, cone, and hemisphere in the ratio form: volume of cone : volume of hemisphere : volume of cylinder = 1 : 2 : 3, and equivalently V₁:V₂:V₃ = 1:2:3.",{"name":88,"@type":79,"acceptedAnswer":89},"If a cylinder’s radius is halved and its height is doubled, what happens to its volume?",{"text":90,"@type":82},"Radius is reduced to half, so cross-sectional area becomes one-fourth; height doubles, so overall volume becomes half of the original.","https://schema.org",{"og:url":53,"og:type":93,"og:title":13,"og:site_name":64,"og:description":14},"article",{"robots":95,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":98},[99,103,107,110,115,120,125,130,135,138,142],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":108,"slug":109},70,"exam",{"id":111,"doc_module":4,"doc_module_name":47,"category_name":112,"show_sort_weight":113,"slug":114},5,"Comic",60,"comic",{"id":116,"doc_module":4,"doc_module_name":47,"category_name":117,"show_sort_weight":118,"slug":119},6,"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":47,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":126,"doc_module":4,"doc_module_name":47,"category_name":127,"show_sort_weight":128,"slug":129},8,"Research & Report",30,"research-report",{"id":131,"doc_module":4,"doc_module_name":47,"category_name":132,"show_sort_weight":133,"slug":134},9,"Religion & Spirituality",20,"religion-spirituality",{"id":133,"doc_module":4,"doc_module_name":47,"category_name":136,"show_sort_weight":133,"slug":137},"World Cup","world-cup",{"id":139,"doc_module":4,"doc_module_name":47,"category_name":140,"show_sort_weight":139,"slug":141},10,"Lifestyle","lifestyle",{"id":143,"doc_module":4,"doc_module_name":47,"category_name":144,"show_sort_weight":111,"slug":145},19,"General","general"]