CHAPTER 12 - Surface Areas and Volumes - Multiple Choice Questions and Short Answer Practice

Sep 18, 2026

Uploaded by Xiajie

Chapter 12 presents core concepts and formulas for surface areas and volumes formed by combining basic solids such as cuboid, cone, cylinder, sphere, and hemisphere. 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 formulas.

LanguageEnglish

CategoryExam

FormatPDF

Pages17

Reading Time43 min

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Multiple Choice Questions

Exercise 12.1

Short Answer Questions with Reasoning

CHAPTER12 SURFACE AREAS AND VOLUMES # (A)Main Concepts and Results · The surface area of an object formed by combining any two of the basic solids,namely,cuboid,cone,cylinder,sphere and hemisphere. · The volume of an object formed by combining any two of the basic solidsnamely,cuboid,cone,cylinder,sphere and hemisphere. · The formulae involving the frustum of a cone are (i) Volume of the frustum of the (ii)Curved surface area of the frustum of the cone =π(r₁+r₂)l, (iii) Total surface area of the frustum of the solid cone,where h=vertical height of the frustum,l =slant height of the frustum andr₁and r₂are radii of the two bases (ends)of the frustum. · Solid hemisphere:If ris the radius of a hemisphere,thencurved surface area =2πr²total surface area=3πr²,and volume · Volume of a spherical,where r₁and r₂are respectively itsexternal and internal radii.,if not stated otherwise.Throughout this chapter,take # (B)Multiple Choice Questions: Choose the correct answer from the given four options: Sample Question 1:A funnel(see Fig.12.1)is thecombination of (A)a cone and a cylinder (C)a hemisphere and a cylinder (D)a hemisphere and a cone Solution :Answer(B) Sample 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 Solution:Answer(A) Sample 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 Solution:Answer(C) Sample 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) Solution :Answer(A) Sample Question 5:The volume of the largest right circular cone that can be cut outfrom a cube of edge 4.2cm is (A)9.7cm³ (B)77.6 cm³ (C)58.2 cm³ (D)19.4 cm³ Solution :Answer(D) Fig.12.1 (B)frustum of a cone and a cylinder (B)a hemisphere and a cylinder EXERCISE12.1 Choose the correct answer from the given four options: 1.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 2.A surahi is the combination of (A)a sphere and a cylinder (C)two hemispheres (D)a cylinder and a cone. 3.A plumbline(sahul)is the combination of (see Fig.12.2) Fig.12.2 (B)a hemisphere and a cone (A)a cone and a cylinder (C)frustum of a cone and a cylinder (D)sphere and cylinder 4.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 Fig.12.3 5.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 Fig.12.4 6.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 7.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 8.A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 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 9.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 10.A solid piece of iron in the form of a cuboid of dimensions 49cm×33cm×2

FAQs

What solids are used in the chapter’s main concepts for surface areas and volumes?

It focuses on cuboid, cone, cylinder, sphere, and hemisphere, including combinations formed from these basic solids.

What key parameters define a frustum of a cone in the chapter?

It uses vertical height h, slant height l, and radii r1 and r2 of the two bases (ends).

How do the questions test understanding in this chapter?

They include multiple choice problems and true/false questions that require applying the given surface area and volume formulas with reasoning.

Sep 18, 2026

Uploaded by Xiajie