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It includes results for frustums of a cone, curved and total surface area expressions, and volume relations for spherical and hemispherical forms. The chapter then provides worked sample problems and an extensive exercise set with multiple choice questions, plus true/false reasoning items to strengthen application of the 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solids are used in the chapter’s main concepts for surface areas and volumes?","Question",{"text":113,"@type":114},"It focuses on cuboid, cone, cylinder, sphere, and hemisphere, including combinations formed from these basic solids.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What key parameters define a frustum of a cone in the chapter?",{"text":118,"@type":114},"It uses vertical height h, slant height l, and radii r1 and r2 of the two bases (ends).",{"name":120,"@type":111,"acceptedAnswer":121},"How do the questions test understanding in this chapter?",{"text":122,"@type":114},"They include multiple choice problems and true/false questions that require applying the given surface area and volume formulas with reasoning.","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},297515,1789745242,{"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},8814010472675,"https://avatar.qwps.com/avatar/WGlhamll","CHAPTER12  \nSURFACE AREAS AND VOLUMES  \n# (A)Main Concepts and Results\n\n·   The surface area of an object formed by combining any two of the basic solids,namely,cuboid,cone,cylinder,sphere and hemisphere.  \n·   The volume of an object formed by combining any two of the basic solidsnamely,cuboid,cone,cylinder,sphere and hemisphere.  \n·  The formulae involving the frustum of a cone are  \n(i)  Volume of the frustum of the  \n(ii)Curved surface area of the frustum of the cone =π(r₁+r₂)l,  \n(iii)  Total surface area of the frustum of the solid cone,where  \nh=vertical height of the frustum,l =slant height of the frustum andr₁and r₂are radii of the two bases (ends)of the frustum.  \n·   Solid hemisphere:If ris the radius of a hemisphere,thencurved surface area =2πr²total surface area=3πr²,and volume  \n·   Volume of a spherical,where r₁and r₂are respectively itsexternal and internal radii.,if not stated otherwise.Throughout this chapter,take  \n# (B)Multiple Choice Questions:\n\nChoose the correct answer from the given four options:  \nSample Question 1:A funnel(see Fig.12.1)is thecombination of  \n(A)a cone and a cylinder  \n(C)a hemisphere and a cylinder (D)a hemisphere and a cone  \nSolution :Answer(B)  \nSample Question2:If a marble of radius 2.1 cm is put into a cylindrical cup full of waterof radius 5cm and height 6cm,then how much water flows out of the cylindrical cup?(B)55.4 cm³(C)19.4 cm³(D)471.4 cm³(A)38.8 cm³  \nSolution:Answer(A)  \nSample Question 3:A cubical ice cream brick of edge 22 cm is to be distributedamong some children by filling ice cream cones of radius 2cm and height 7 cm upto itsbrim.How many children will get the ice cream cones?(B)263(C)363(D)463(A)163  \nSolution:Answer(C)  \nSample Question 4:The radii of the ends of a frustum of a cone of height h cm arer,cm and r₂cm.The volume in cm³of the frustum of the cone is(A)(C)  \nSolution :Answer(A)  \nSample Question 5:The volume of the largest right circular cone that can be cut outfrom a cube of edge 4.2cm is  \n(A)9.7cm³  \n(B)77.6 cm³  (C)58.2 cm³  (D)19.4 cm³  \nSolution :Answer(D)  \nFig.12.1  \n(B)frustum of a cone and a cylinder  \n(B)a hemisphere and a cylinder  \nEXERCISE12.1  \nChoose the correct answer from the given four options:  \n1.A cylindrical pencil sharpened at one edge is the combination of(B)frustum of a cone and a cylinder(A)a cone and a cylinder(D)two cylinders.(C)a hemisphere and a cylinder  \n2.A surahi is the combination of  \n(A)a sphere and a cylinder  \n(C)two hemispheres  \n(D)a cylinder and a cone.  \n3.A plumbline(sahul)is the combination of (see Fig.12.2)  \nFig.12.2  \n(B)a hemisphere and a cone  \n(A)a cone and a cylinder  \n(C)frustum of a cone and a cylinder  \n(D)sphere and cylinder  \n4.The shape of a glass (tumbler)(see Fig.12.3)is usually in the form of(B)frustum of a cone(A)a cone(D)a sphere(C)a cylinder  \nFig.12.3  \n5.The shape of a gilli,in the gilli-danda game (see Fig.12.4),is a combination of(A)two cylinders(B)a cone and a cylinder(C)two cones and a cylinder(D)two cylinders and a cone  \nFig.12.4  \n6.A shuttle cock used for playing badminton has the shape of the combination of(A)a cylinder and a sphere(B)a cylinder and a hemisphere(C)a sphere and a cone(D)frustum of a cone and a hemisphere  \n7.A cone is cut through a plane parallel to its base and then the cone that is formedon one side of that plane is removed.The new part that is left over on the otherside of the plane is called(A)a frustum of a cone(B)cone(C)cylinder(D)sphere  \n8.A hollow cube of internal edge 22cm is filled with spherical marbles of diameter  \n0.5 cm and it is assumed thatspace of the cube remains unfilled.Then thenumber of marbles that the cube can accomodate is(A)142296(B)142396(C)142496(D)142596  \n9.A metallic spherical shell of internal and external diameters 4cm and 8 cm,respec-tively is melted and recast into the form a cone of base diameter 8cm.The height ofthe cone is(A)12cm(B)14cm(C)15cm(D)18cm  \n10.A solid piece of iron in the form of a cuboid of dimensions 49cm×33cm×2","cbCaiqj66Wt8VbMy","https://ap.wps.com/l/cbCaiqj66Wt8VbMy","pdf",12262895,17,"English","# Multiple Choice Questions\n## Exercise 12.1\n# Short Answer Questions with Reasoning","[{\"question\":\"What solids are used in the chapter’s main concepts for surface areas and volumes?\",\"answer\":\"It focuses on cuboid, cone, cylinder, sphere, and hemisphere, including combinations formed from these basic solids.\"},{\"question\":\"What key parameters define a frustum of a cone in the chapter?\",\"answer\":\"It uses vertical height h, slant height l, and radii r1 and r2 of the two bases (ends).\"},{\"question\":\"How do the questions test understanding in this chapter?\",\"answer\":\"They include multiple choice problems and true/false questions that require applying the given surface area and volume formulas with reasoning.\"}]","CHAPTER 12 - Surface Areas and Volumes - Multiple Choice Questions and Short Answer Practice | PDF",43]