CBSE 10th Maths Exam 2021: Important MCQs from Chapter 13 Surface Areas and Volumes with Detailed Solutions

MCQ on Surface Areas and Volumes Class 10 are very important for all students who want to score good marks in their Class 10 Maths CBSE Exam. You can practice these solved objective type questions to brush up on your basic math skills. Anyone with Standard or Basic Mathematics can refer to these questions as a practice test for their CBSE Board Exam.

Note - Students must note that 'Frustum of a cone' has been excluded from the revised CBSE syllabus of Class10 Maths. So, students should prepare according to the new syllabus only.

Check below the solved MCQs from Class 10 Maths Chapter 13 Surface Areas and Volumes:

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.

Answer: (A)

Explanation: The shape of a sharpened pencil is:

2. A cone is cut through a plane parallel to its base and then the cone that is for medon 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

Answer:  (A)

Explanation: Observe figure

3. 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

Answer:  (C)

Explanation: During conversion of one solid shape to another, the volume of the new shape will remain unaltered.

Also Read: CBSE Class 10 Science Important MCQs for Board Exam 2021

4. A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter

(A) r cm

(B) 2r cm

(C) h cm

(D) 2h cm

Answer: (B)

Explanation: Because the sphere is enclosed inside the cylinder, therefore the diameter of sphere is equal to the diameter of cylinder which is 2r cm.

5. A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8th space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is

(A) 142244

(B) 142396

(C) 142496

(D) 142596

Answer:  (A)

Explanation:

6. A metallic spherical shell of internal and external diameters 4 cm and 8 cm respectively, is melted and recast into the form of a cone with base diameter 8cm. The height of the cone is

(A) 12cm

(B) 14cm

(C) 15cm

(D) 18cm

Answer:  (B)

Explanation:Since volume will remain same, therefore,

7. A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is

(A) 21cm

(B) 23cm

(C) 25cm

(D) 19cm

Answer:  (A)

Explanation: Since volume will remain the same, therefore,

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

(A) 4πr²

(B) 6πr²

(C) 3πr²

(D) 8πr²

Answer:  (A)

Explanation: Because curved surface area of a hemisphere is and here we join two solid hemispheres along their bases of radii r, from which we get a solid sphere.

Hence the curved surface area of new solid = 2πr² + 2πr² = 4πr²

9. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is

(A) 4πrh + 4πr²

(B) 4πrh − 4πr²

(C) 4πrh + 2πr²           

(D) 4πrh − 2πr²

Answer:  (C)

Explanation: Since the total surface area of cylinder of radius r and height h = 2πrh + 2πr².

When one cylinder is placed over the other cylinder of same height and radius,

Then height of new cylinder = 2h

And radius of the new cylinder = r

Therefore total surface area of new cylinder

= 2πr (2h) + 2πr²

= 4πrh + 2πr²

CBSE Class 10 Maths New Exam Pattern 2021: Check to Score High in Exam

10. The radii of the top and bottom of a bucket of slant height 45cm are 28cm and 7 cm respectively. The curved surface area of the bucket is:

(A) 4950 cm²

(B) 4951 cm²

(C) 4952 cm²

(D) 4953 cm²

Answer: (A)

Explanation:

Curved Surface area of the bucket = π (R + r) l

⇒ Curved surface area of the bucket = π (28 + 7) X 45

⇒ Curved surface area of the bucket = 4950 cm²

11. A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is

(A) 0.36 cm³

(B) 0.35 cm³

(C) 0.34 cm³

(D) 0.33 cm³

Answer:  (A)

Explanation:

Since diameter of the cylinder = diameter of the hemisphere = 0.5cm

Radius of cylinder r = radius of hemisphere r = 0.5/2 = 0.25 cm

Observe the figure,

Total length of capsule = 2cm

Capacity of capsule is:

CBSE Class 10th Maths Chapter-wise Important Formulas, Theorems & Properties

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

(A) 4 cm

(B) 3 cm

(C) 2 cm

(D) 6 cm

Answer:  (C)

Explanation:

Therefore diameter of each solid sphere = 2cm

13. The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is

(A) 32.7 litres

(B) 33.7 litres

(C) 34.7 litres

(D) 31.7 litres

Answer:  (A)

Explanation: Since shape of bucket is like Frustum,

Therefore, volume of bucket

CBSE Class 10 Science Important Questions of All Formats for Board Exam 2021

14. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is:

(A) 3 : 4

(B) 4 : 3

(C) 9 : 16

(D) 16 : 9

Answer: (D)

Explanation: According to question,

 

Therefore ratio of surface area is:

15. 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) 11300

Answer:  (B)

Explanation: According to question,

You can also download all of the above questions in PDF format form the link provided below so that you are able to practice these questions in offline mode according to your convenience.

To check the important MCQs from all other chapters of CBSE Class 10 Maths, go to the following link:

CBSE Class 10 Maths Important MCQs: All Chapters

Also check important resources for the preparation of CBSE Class 10 Board Exam 2021:

To make your preparations for the CBSE Class 10 Board Exam easy and organised, we at Jagran Josh are bringing together some important resources. These resources are enough to make you familiar with the format of examination and what you may expect from the exam so that you can make your preparations according to the same. Important links are provided below:

• CBSE Class 10 Exam Pattern 2021: All Subjects
• CBSE Class 10 Syllabus for Board Exam 2021: All Subjects
• CBSE Class 10 Sample Papers with Marking Scheme 2021: All Subjects
• CBSE Class 10 Question Papers 2020 with Solutions
• CBSE Class 10 NCERT Exemplar Problems, Solutions for Maths & Science
• CBSE Class 10 NCERT New Textbooks & NCERT Solutions: All Subjects