Here you get the CBSE Class 10 Mathematics chapter 12, Surface Areas and Volumes: NCERT Exemplar Problems and Solutions (Part-IA). This part of the chapter includes solutions to Q. No. 1 to 9 from Exercise 12.1 of NCERT Exemplar Problems for Class 10 Mathematics. This exercise comprises only the Multiple Choice Questions (MCQs) framed from various important topics in the chapter. Each question is provided with a detailed solution.

**CBSE Class 10 Mathematics Syllabus 2017-2018**

NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.

**Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Surface Areas and Volumes:**

**Exercise 12.1**

**Multiple Choice Questions (Q. No. 1-10)**

**Question. 1 **A cylindrical pencil sharpened at one edge is the combination of

(a) a cone and a cylinder

(b) frustum of a cone and a cylinder

(c) a hemisphere and a cylinder

(d) two cylinders

**Solution. ( a)**

**Explanation:**

A cylindrical pencil sharpened at one edge is the combination of a cone and a cylinder as shown below:

**Question. 2 **A surahi is the combination of

(a) a sphere and a cylinder

(b) a hemisphere and a cylinder

(c) two hemispheres

(d) a cylinder and a cone

**Solution.**

**Explanation:**

The lower portion of a surahi is a sphere and its upper part (neck) is in cylindrical shape.

(a) a cone and a cylinder

(b) a hemisphere and a cone

(c) frustum of a cone and a cylinder

(d) sphere and cylinder

**Solution. (b)**

**Explanation:** Base of a plumbline is a cone and its top is a hemisphere.

(a) a* *cone

(b) frustum of a cone

(c) a cylinder

(d) a sphere

**Solution. (b)**

**Explanation: **

The shape of a glass (tumbler) is usually in the form of a frustum as the frustum of a cone is the shape obtained obtained by cutting a right circular cone by a plane parallel to the base of the cone.

**Question. 5 **The shape of a gilli, in the gilli-danda game (see figure) is a combination of

**Question. 6 **A shuttle cock used for playing badminton has 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

**Solution. (d)*** *

**Explanation:**

The shape of the shuttle cock is in the form of the frustum of a cone and a hemisphere.

**Question. 7 **A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that

plane is removed. The new part that is left over on the other side of the plane is called

(a) a frustum of a cone

(b) cone

(c) cylinder

(d) sphere

**Solution. (a) **

**Explanation: **

When a cone is through the plane parallel to its base then the part other than the cone is called the frustum of a cone.

**Question. 8 **If a hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5cm and it is assumed that space of the cube remains unfilled. Then, the number of marbles that the cube can accomodate is

(a) 142244

(b) 142344

(c) 142444

(d) 142544

**Solution. (a)*** *

**Explanation: **

Given, edge of the cube = 22cm

∴ Volume of the cube = (side)^{3} = (22)^{3} = 10648cm^{3}

Also, given diameter of marble = 0.5cm

**Question. 9 **A metallic spherical shell of internal and external diameters 4cm and 8cm, respectively is melted and

recast into the form a cone of base diameter 8cm. The height of the cone is

(a) 12cm

(b) 14cm

(c) 15cm

(d) 18cm

**Solution. ****(b)*** *

**Explanation: **

Given, internal diameter of spherical shell = 4cm

And external diameter of shell = 8cm

∴ Internal radius of spherical shell, *r*_{1}* *= 4/2 = 2cm

And external radius of shell, *r*_{2}* *= 8/2 = 4 cm

**Question. 10 **If a solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. Then, radius of the sphere is

(a) 21cm

(b) 23cm

(c) 25cm

(d) 19cm

**Solution. (a)*** *

**Explanation:**

As a cuboid is moulded to form a sphere,

Hence, the radius of the sphere is 21cm.

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