Mensuration (Part-7)

1. The breadth of a room is twice its height and half its length. The volume of the room is 1728 m³. The length of the room is: [SSC CPO 29/06/2024 (1st Shift)]

(a) 20 m
(b) 24 m
(c) 34m
(d) 28 m

Correct Answer: (b) 24 m

Solution:

2. A woman working in a company was supplied a rectangular solid (cuboid shape) of wax with dimensions 70 cm, 44 cm and 20 cm to prepare cylindrical candles, each 14 cm in diameter and 20 cm of height. Find the number of candles. [SSC CPO 29/06/2024 (1st Shift)]

(a) 15
(b) 20
(c) 10
(d) 30

Correct Answer: (b) 20

Solution:

3. A cone of slant height 4.2 units has a lateral surface area 13.2 units² The radius of the base is: [SSC CPO 29/06/2024 (1st Shift)]

(a) 1 unit
(b) 1.5 units
(c) 2.5 units
(d) 2 units

Correct Answer: (a) 1 unit

Solution:

4. The in-radius of a triangle is 8 cm, and the sum of the lengths of its sides is 125 cm. The area of the triangle (in cm²) is [SSC CPO 29/06/2024 (2nd Shift)]

(a) 480
(b) 1000
(c) 250
(d) 500

Correct Answer: (d) 500

Solution:

5. Melting a metal ball of radius 3 units, 27 identical dice and a ball of radius 1 units are made. What is the side of dice? [SSC CPO 29/06/2024 (2nd Shift)]

(a) 1.7 units
(b) 1.5 units
(c) 1.6 units
(d) 1.4 units

Correct Answer: (c) 1.6 units

Solution:

6. The ratio of the slant height and the height of a cone is 4:3. If the curved surface area of the cone is 4√3 π square units, then the radius of the cone is_______units. [SSC CPO 29/06/2024 (3rd Shift)]

(a) 7√7
(b) 7
(c) √7
(d) √7/7

Correct Answer: (c) √7

Solution:

7. The length of a side of an equilateral triangle is 18 cm. The area (in cm²) of the region lying between the circumcircle and the incircle of the triangle is [use π = 22/7] [SSC CPO 29/06/2024 (3rd Shift)]

Correct Answer: (d)

Solution:

8. The area of a circle is 256π square cm. The length of its longest chord (in cm) is: [SSC CPO 29/06/2024 (3rd Shift)]

(a) 34
(b) 36
(c) 6
(d) 32

Correct Answer: (d) 32

Solution:

9. The perimeter of one face of a cube is 40 cm. Its volume will be: [Matriculation Level 20/06/2024 (Shift-1)]

(a) 10 cm³
(b) 100 cm³
(c) 1000 cm³
(d) 10000 cm³

Correct Answer: (c) 1000 cm³

Solution:

10. If the length of each of the two equal sides of an isosceles triangle is 15 cm and the adjacent angle is 30°, then the area of the triangle is: [Matriculation Level 20/06/2024 (Shift-1)]

(a) 66.25 cm²
(b) 36.25 cm²
(c) 56.25 cm²
(d) 26.25 cm²

Correct Answer: (c) 56.25 cm²

Solution:

Mensuration (Part-7)

1. The breadth of a room is twice its height and half its length. The volume of the room is 1728 m³. The length of the room is: [SSC CPO 29/06/2024 (1st Shift)]

2. A woman working in a company was supplied a rectangular solid (cuboid shape) of wax with dimensions 70 cm, 44 cm and 20 cm to prepare cylindrical candles, each 14 cm in diameter and 20 cm of height. Find the number of candles. [SSC CPO 29/06/2024 (1st Shift)]

3. A cone of slant height 4.2 units has a lateral surface area 13.2 units² The radius of the base is: [SSC CPO 29/06/2024 (1st Shift)]

4. The in-radius of a triangle is 8 cm, and the sum of the lengths of its sides is 125 cm. The area of the triangle (in cm²) is [SSC CPO 29/06/2024 (2nd Shift)]

5. Melting a metal ball of radius 3 units, 27 identical dice and a ball of radius 1 units are made. What is the side of dice? [SSC CPO 29/06/2024 (2nd Shift)]

6. The ratio of the slant height and the height of a cone is 4:3. If the curved surface area of the cone is 4√3 π square units, then the radius of the cone is_______units. [SSC CPO 29/06/2024 (3rd Shift)]

7. The length of a side of an equilateral triangle is 18 cm. The area (in cm²) of the region lying between the circumcircle and the incircle of the triangle is [use π = 22/7] [SSC CPO 29/06/2024 (3rd Shift)]

8. The area of a circle is 256π square cm. The length of its longest chord (in cm) is: [SSC CPO 29/06/2024 (3rd Shift)]

9. The perimeter of one face of a cube is 40 cm. Its volume will be: [Matriculation Level 20/06/2024 (Shift-1)]

10. If the length of each of the two equal sides of an isosceles triangle is 15 cm and the adjacent angle is 30°, then the area of the triangle is: [Matriculation Level 20/06/2024 (Shift-1)]

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