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It summarizes key formulas such as volume and total/curved surface area, plus relationships involving diagonals. The exercises then provide multiple-choice questions and true/false problems that test scaling rules (e.g., radius and height changes) and applications to word problems involving storage, balloons, poles, and geometric conversions between solids.",{"@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-areas-and-volumes-chapter-13-multiple-choice-questions/297703/",{"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-areas-and-volumes-chapter-13-multiple-choice-questions/297703.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",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the formula for the volume and total surface area of a cuboid?","Question",{"text":113,"@type":114},"For a cuboid with length l, breadth b, and height h, the volume is lbh and the total surface area is 2(lb+bh+hl).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does changing radius and height affect a cylinder’s volume?",{"text":118,"@type":114},"For a cylinder, volume is proportional to r^2h, so halving the radius and doubling the height changes the factor by (1/2)^2×2=1/2, meaning the volume becomes halved.",{"name":120,"@type":111,"acceptedAnswer":121},"What does the chapter ask students to do in the true/false reasoning section?",{"text":122,"@type":114},"Students must mark each statement as True or False and justify the answer using the given geometric relationships and formulas for the solids.","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},297703,1789747214,{"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":39,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":46},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","SURFACE AREAS AND VOLUMES  \n# (A)Main Concepts and Results\n\n·Cuboid whose length =l,breadth=b and height=h  \n(a)Volume of cuboid=lbh  \n(b)Total surface area of cuboid=2(lb+bh+hl)  \n(c)Lateral surface area of cuboid=2h(l+b)  \n(d)Diagonal of cuboid=√i²+b²+h²  \n·Cube whose edge =a  \n(a)Volume of cube =a³  \n(b)Lateral Surface area =4a²  \n(c)Total surface area of cube =6a²  \n(d)Diagonal of cube=a√3  \n·Cylinder whose radius=r,height =h  \n(a)Volume of cylinder=πr²h  \n(b)Curved surface area of cylinder =2πrh  \n(c)Total surface area of cylinder=2πr(r+h)  \n·Cone having height =h,radius =r and slant height =l  \n(b)Curved surface area of cone =πrl  \nCHAPTER 13  \n(c)Total surface area of cone=πr(l+r)  \n(d)Slant height of cone  \n·Sphere whose radius =r  \n(b)Surface area of sphere =4πr²  \n·Hemisphere whose radius =r  \n(b)Curved surface area of hemisphere =2πr²  \n(c)Total surface area of hemisphere=3πr²  \n# (B)Multiple Choice Questions\n\nWrite the correct answer  \nSample Question 1:In a cylinder,if radius is halved and height is doubled,thevolume will be(A)  same(B)  doubled    (C)  halved(D)  four times  \nSolution:Answer(C)  \n# EXERCISE 13.1\n\nWrite the correct answer in each of the following:  \n1.The radius of a sphere is 2r,then its volume will be(B)  4πr³(A)(C)D)  \n2.The total surface area of a cube is 96cm².The volume of the cube is:(C)  64 cm³(A)  8 cm³(B)  512cm³D)  27 cm³  \n3.A cone is 8.4 cm high and the radius of its base is 2.1 cm.It is melted and recastinto a sphere.The radius of the sphere is:(A)  4.2cm(B)  2.1 cm(C)  2.4 cm(D)  1.6cm  \n4.In a cylinder,radius is doubled and height is halved,curved surface area willbe  \n(B)  doubled  \n(C)  same  \n(A)halved  \n5.The total surface area of a cone whose radius isand slant height 2l isπr(+)(C)πr(l+r)(D)2πrl(A)2πr(l+r)(B)  \n6.The radii oftwo cylinders are in the ratio of 2:3 and their heights are in the ratio of  \n5:3.The ratio of their volumes is:  \n(A)10:17  \n(B)20:27  \n(C)  17:27  \n7.The lateral surface area of a cube is 256 m².The volume of the cube is(A)512m³(B)64 m³(D)256m³(C)216m³  \n8.The number of planks of dimensions(4m×50cm×20cm)that can be stored ina pit which is 16m long,12m wide and 4m deep is(A)1900(B)  1920(C)  1800(D)1840  \n9.The length of the longest pole that can be put in a room of dimensions(10m×10m×5m)is(A)15m(B)  16m(C)10m(D)12m  \n10.The radius of a hemispherical balloon increases from6cm to 12cm as air is beingpumped into it.The ratios of the surface areas of the balloon in the two cases is(A)1:4(B)1:3(C)2:3(D)  2:1  \n# (C)ShortAnswerQuestions with Reasoning\n\nWrite True or False and justify your answer.  \nSample Question 1:Aright circular cylinder just encloses a sphereof radius ras shown in Fig 13.1.The surface area of the sphere isequal to the curved surface area of the cylinder.  \nSolution:True.  \nHere,radius of the sphere=radius of the cylinder=rDiameter of the sphere=height of the cylinder=2rSurface area of the sphere =4πr²Curved surface area of the cylinder=2πr(2r)=4πr²  \nSample Question 2:An edge of a cube measures rcm.If the largest possible rightcircular cone is cut out of this cube,then the volume of the cone (in cm³is  \nD)four times  \n(D)20:37  \nFig 13.1→  \nSolution:False.  \nHeight of the cone =rcm.  \nDiameter of the base =rcm.  \nTherefore,volume of the cone  \nEXERCISE13.2  \nWrite True or False and justify your answer in each of the following:  \n1.The volume of a sphere is equal to two-third of the volume of a cylinder whoseheight and diameter are equal to the diameter of the sphere.  \n2.If theradius of aright circular cone is halved and height is doubled,the volume willremain unchanged.  \n3.In a right circular cone,height,radius and slant height do not always be sides of aright triangle.  \n4.If the radius of a cylinder is doubled and its curved surface area is not changed,the height must be halved.  \n5.The volume of the largest right circular cone that can be fitted in a cube whoseedge is 2r equals to the volume of a hemisphere of radius r.  \n6.A cylinder","cbCaimcVWAwtUuaa","https://ap.wps.com/l/cbCaimcVWAwtUuaa","pdf",145591,"English","# (A) Main Concepts and Results\n## Cuboid, Cube, Cylinder, Cone, Sphere, Hemisphere formulas\n# (B) Multiple Choice Questions\n## Sample Question 1\n# EXERCISE 13.1\n## Radius/height scaling and surface/volume combinations\n# (C) Short Answer Questions with Reasoning\n## True or False with justification\n# EXERCISE 13.2\n## Reasoning statements about solids\n# (D) Short Answer Questions\n## Worked examples and proofs\n# EXERCISE 13.3","[{\"question\":\"What is the formula for the volume and total surface area of a cuboid?\",\"answer\":\"For a cuboid with length l, breadth b, and height h, the volume is lbh and the total surface area is 2(lb+bh+hl).\"},{\"question\":\"How does changing radius and height affect a cylinder’s volume?\",\"answer\":\"For a cylinder, volume is proportional to r^2h, so halving the radius and doubling the height changes the factor by (1/2)^2×2=1/2, meaning the volume becomes halved.\"},{\"question\":\"What does the chapter ask students to do in the true/false reasoning section?\",\"answer\":\"Students must mark each statement as True or False and justify the answer using the given geometric relationships and formulas for the solids.\"}]","SURFACE AREAS AND VOLUMES - CHAPTER 13 - Multiple Choice Questions | PDF"]