Mensuration (Part-14)

Total Questions: 50

1. A solid metallic cuboid of dimensions 12cm × 54cm × 72 cm is melted and converted into 8 cubes of the same size. What is the sum of the lateral surface areas (in cm²) of 2 such cubes? [SSC CGL Tier II (29/01/2022)]

Correct Answer: (a) 2592
Solution:

2. The radius of a spherical balloon is inflated from 3.5 cm to 4.9 cm by pushing air into it. What is the percentage increase in the volume of the original balloon? [SSC CGL Tier II (29/01/2022)]

Correct Answer: (b) 174.4%
Solution:

3. The radius of the base of a cylindrical tank is 4 m. If three times the sum of the areas of its two circular faces is twice the area of its curved surface, then the capacity (in kilolitres) of the tank is: [SSC CGL Tier II (29/01/2022)]

Correct Answer: (c) 96π
Solution:

4. The slant height and radius of a right circular cone are in the ratio 29:20. If its volume is 4838.4 cm³, then its radius is: [SSC CGL Tier II (29/01/2022)]

Correct Answer: (c) 24 cm
Solution:

5. The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm², 96 cm² and 144 cm². It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm²) rangle of 3 such cubes? [SSC CGL Tier II (03/02/2022)]

Correct Answer: (b) 432
Solution:

6. A well with inner radius 3 m, is dug 6 m deep. The soil taken out of it has been spread evenly all around it to a width of 2 m to form an embankment. The height (in m) of the embankment is: [ SSC CGL Tier II (03/02/2022)]

Correct Answer: (d)
Solution:

7. A solid metallic sphere of radius 4 cm is melted and recast into spheres of 2 cm each. What is the ratio of the surface area of the original sphere to the sum of surface areas of the spheres, so formed? [SSC CGL Tier II (03/02/2022)]

Correct Answer: (c) 1:2
Solution:

8. A cylindrical tube, open at both ends, is made of a metal sheet which is 0.5 cm thick. Its outer radius is 4 cm and length is 2 m. How much metal (in cm³) has been used in making the tube ? [SSC CGL Tier II (03/02/2022)]

Correct Answer: (c) 750π
Solution:

9. The base of a right prism is a triangle whose sides are 8 cm, 15 cm and 17 cm, and its lateral surface area is 480cm². What is the volume (in cm³) of the prism? [SSC CGL Tier II (03/02/2022)]

Correct Answer: (c) 720
Solution:

10. The curved surface area of a right 2 circular cone is 2310 cm² and its radius is 21 cm. If its radius is increased by 100% and height is reduced by 50%, then its capacity (in litres) will be correct to one decimal place) (User π = 22/7) [SSC CGL Tier II (03/02/2022)]

Correct Answer: (d) 25.9
Solution: