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Mensuration Aptitude Questions & Formulas with answer


Ques 1 GATE 2026

The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was 2.5 stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length AB). This was surrounded by two pairs of alternating rings of land and water. The first pair of land and water was two stades wide each (lengths BC and CD), and the outer pair is three stades wide each (lengths DE and EF).

The ratio of the surface area of the land to that of the water in the city of Atlantis is _________ (round off to two decimal places).

A

0.45

B

0.60

C

0.75

D

0.90

() is the correct answer.

Ques 2 GATE 2023 SET-1

In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in cm2) of the shaded region? (The diagram is representative)

A

25π⁄3

B

20π⁄3

C

6π

D

7π

(a) is the correct answer.

Ques 3 GATE 2023 SET-1

A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown. The area of the shaded region is _______ cm2.

A

8

B

4

C

12

D

10

(a) is the correct answer.

Ques 4 GATE 2023

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is _______ cm2.

A

6π

B

18

C

20

D

9π

(b) 18) is the correct answer.

Ques 5 GATE 2022

A sphere of radius 𝑟 cm is packed in a box of cubical shape. What should be the minimum volume (in cm3 ) of the box that can enclose the sphere?

A

r³/8

B

r³

C

2r³

D

8r³

(d) is the correct answer.

Ques 6 GATE 2021

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is

A

π/2

B

3/π

C

9/π

D

3π

(c) is the correct answer.

Ques 7 GATE 2021

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $cm^{2}$ is:

A

12.50

B

6.25

C

3.125

D

1.5625

(b) is the correct answer.

Ques 8 GATE 2021

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is ___________.

A

π/2

B

3/π

C

9/π

D

3π

(c) is the correct answer.

Ques 9 GATE 2019

The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is _______.

A

17.1

B

21.0

C

33.1

D

72.8

(c) is the correct answer.

Ques 10 GATE 2018

The area of an equilateral triangle is √3. What is the perimeter of the triangle?

A

2

B

4

C

6

D

8

(c) is the correct answer.

Ques 11 GATE 2018

Arrange the following three-dimensional objects in the descending order of their volumes:
(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm
(ii) A cube of side 8 cm
(iii) A cylinder with base radius 7 cm and height 7 cm
(iv) A sphere of radius 7 cm

A

(i), (ii), (iii), (iv)

B

(ii), (i), (iv), (iii)

C

(iii), (ii), (i), (iv)

D

(iv), (iii), (ii), (i)

(d) is the correct answer.

Ques 12 GATE 2016 SET-1

A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is

A

56

B

64

C

72

D

96

(d) is the correct answer.


Question Options

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