NCERT Exemplar Solution for CBSE Class 10 Mathematics: Surface Areas and Volumes (Part-IB)

Here you get the CBSE Class 10 Mathematics chapter 12, Surface Areas and Volumes: NCERT Exemplar Problems and Solutions (Part-IB). This part of the chapter includes solutions of Question Number 11 to 20 from Exercise 12.1 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Surface Areas and Volumes. 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.

NCERT Exemplar Solution for CBSE Class 10 Mathematics: Surface Areas and Volumes (Part-IA)

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. 11-20):

Question.11 A mason constructs a wall of dimensions 270cm × 300cm × 350cm with the bricks each of size 22.5cm × 11.25cm × 8.75cm and it is assumed that 1/8  space is covered by the mortar. Then, the number of bricks

used to construct the wall is

(a) 11100             

(b) 11200             

(c) 11000              

(d) 11 300

Solution. (b)        

Explanation:

Volume of the wall = 270 × 300 × 350 = 28350000cm³

And, volume of one brick = 22.5 × 11.25 × 8.75 = 2214.84cm³

Given, volume of the wall covered by mortar = 1/8 part

 

 

Question.12 Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm. The diameter of each sphere is

(a) 4cm                                                                             

(b) 3cm                                                                             

(c) 2cm                                                                             

(d) 6cm

Solution. (c)         

Explanation:

Question. 13 The radii of the top and bottom of a bucket of slant height 45cm are 28cm and 7cm, respectively. The

curved surface area of the bucket is

(a) 4950cm²         

(b) 4951cm²              

(c) 4952cm²              

(d) 4953cm²

Solution. (a)

Explanation:

Given, the radius of top of the bucket, r₁ = 28cm

Radius of the bottom of the bucket, r₂ = 7cm

And, slant height of the bucket, l = 45cm

As a bucket is in the from of a frustum of a cone,

 

Question. 14 A medicine-capsule is in the shape of a cylinder of diameter 0.5cm with two hemispheres stuck to

each of its ends. The length of entire capsule is 2cm. The capacity of the capsule is

(a) 0.36cm³          

(b) 0 35cm³          

(c) 0.34cm³          

(d) 0.33cm³

Solution. (a)        

 

Question. 15 If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is

(a) 4πr² 

(b) 6πr² 

(c) 3πr²  

(d) 8πr²

Solution. (a)

Explanation:

As two solid hemispheres of same base radius r are joined together along their bases then the new solid formed will be a sphere with the same radius r.

∴Curved surface area of the sphere = πr²

Question. 16 A right circular cylinder of radius r cm and height h cm (where, h > 2r) just encloses a sphere of Diameter

(a) r cm 

(b) 2r cm              

(c) h cm

(d) 2h cm

Solution. (b)        

Explanation:

For a sphere just enclosed in a cylinder, its diameter will be equal to the diameter of cylinder whichis 2r cm.

                                                                     

Question. 17 During conversion of a solid from one shape to another, the volume of the new shape will

(a) increase          

(b) decrease

(c) remain unaltered           

(d) be doubled

Sol. (c)  

Explanation:

When a solid is converted from one shape to another, the volume of the new shape will remain unaltered (same).

Question. 18 The diameters of the two circular ends of the bucket are 44cm and 24cm. The height of the bucket is

35cm. The capacity of the bucket is

(a) 32.7 L             

(b) 33.7 L             

(c) 34.7 L              

(d) 31.7 L

Solution. (a)

Explanation:

Given, Height of the bucket, h = 35cm

And diameters of the two circular ends of the bucket are 44cm and 24cm.

 

 

Question. 19 In a right circular cone, the cross-section made by a plane parallel to the base is a

(a) circle

(b) frustum of a cone         

(c) sphere              

(d) hemisphere

Solution. (b)

Explanation. If a right circular cone is cut by a plane parallel to the base then the cross-section obtained is a circle.

Question. 20 If volumes of two spheres are in the ratio 64:27, then the ratio of their surface areas is

(a) 3:4   

(b) 4:3   

(c) 9:6   

(d) 16:9

Solution. (d)

Ratio of volumes of two sphere is given as,

                 

 

CBSE Class 10 Mathematics Syllabus 2017-2018

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