Mensuration (Part-8)

11. If the slant height of a cone is 29 cm and its height is 20 cm, find the ratio between the magnitudes of total surface area and the volume. [SSC CPO 05/10/2023 (3rd Shift)]

(a) 3:7
(b) 3:14
(c) 5:14
(d) 7:15

Correct Answer: (c) 5:14

Solution:

12. The radius of a metallic spherical ball is 3 cm. If the metallic ball is melted and recast into x number of hemispheres of radius equal to half the radius of the metallic spherical ball, then find the value of x. [SSC CPO 05/10/2023 (3rd Shift)]

(a) 14
(b) 16
(c) 13
(d) 15

Correct Answer: (b) 16

Solution:

13. A hollow cylindrical tube made of plastic is 3 cm thick. If the external diameter is 20 cm and length of the tube is 49 cm, find the volume of the plastic. [SSC CPO 05/10/2023 (3rd Shift)]

(a) 7644 cm³
(b) 7238 cm³
(c) 7854 cm³
(d) 7546 cm³

Correct Answer: (c) 7854 cm³

Solution:

14. The diameter of a metallic sphere is 6 cm. It is melted and drawn into a wire having a diameter of the cross section as 0.4 cm. Find the length of the wire (in meters). [SSC MTS 01/09/2023 (1st Shift)]

(a) 18
(b) 9
(c) 12
(d) 10

Correct Answer: (b) 9

Solution:

15. From a cuboid of dimension of 8 x 6 x 6 units, small cubes of dimension 0.5 x 0.5 x 0.5 unit are cut. How many small cubes can be cut from the big cuboid? [SSC MTS 01/09/2023 (3rd Shift)]

(a) 576
(b) 1152
(c) 2304
(d) 1552

Correct Answer: (c) 2304

Solution:

16. The radius and the height of a right circular cone are in the ratio 3: 4. If its volume is 301.44m³, find the slant height (use π = 3.14). [SSC MTS 04/09/2023 (1st Shift)]

(a) 5 cm
(b) 20 cm
(c) 10 cm
(d) 15 cm

Correct Answer: (c) 10 cm

Solution:

17. Water is pouring into a cuboidal reservoir at the rate of 50 litres per minute. The volume of the reservoir is 120 m³. How many hours will it take to fill the reservoir ? [SSC MTS 04/09/2023 (3rd Shift)]

(a) 35
(b) 45
(c) 40
(d) 30

Correct Answer: (c) 40

Solution:

18. Using the middle points of sides of a square with an area of 36 square units, another square is made. What is the area of a new square made in square units? [SSC MTS 05/09/2023 (2nd Shift)]

(a) 24
(b) 27
(c) 18
(d) 21

Correct Answer: (c) 18

Solution:

19. The length of the median of an equilateral triangle is 6√3 cm. The area of the triangle is: [SSC MTS 05/09/2023 (3rd Shift)]

(a) 36√3 cm²
(b) 36 cm²
(c) 72 cm²
(d) 72√3 cm²

Correct Answer: (a) 36√3 cm²

Solution:

20. The areas of three adjacent faces 2 of a cuboid are p, q and r unit², respectively. What is its volume? [SSC MTS 06/09/2023 (3rd Shift)]

Correct Answer: (b)

Solution:

Mensuration (Part-8)

11. If the slant height of a cone is 29 cm and its height is 20 cm, find the ratio between the magnitudes of total surface area and the volume. [SSC CPO 05/10/2023 (3rd Shift)]

12. The radius of a metallic spherical ball is 3 cm. If the metallic ball is melted and recast into x number of hemispheres of radius equal to half the radius of the metallic spherical ball, then find the value of x. [SSC CPO 05/10/2023 (3rd Shift)]

13. A hollow cylindrical tube made of plastic is 3 cm thick. If the external diameter is 20 cm and length of the tube is 49 cm, find the volume of the plastic. [SSC CPO 05/10/2023 (3rd Shift)]

14. The diameter of a metallic sphere is 6 cm. It is melted and drawn into a wire having a diameter of the cross section as 0.4 cm. Find the length of the wire (in meters). [SSC MTS 01/09/2023 (1st Shift)]

15. From a cuboid of dimension of 8 x 6 x 6 units, small cubes of dimension 0.5 x 0.5 x 0.5 unit are cut. How many small cubes can be cut from the big cuboid? [SSC MTS 01/09/2023 (3rd Shift)]

16. The radius and the height of a right circular cone are in the ratio 3: 4. If its volume is 301.44m³, find the slant height (use π = 3.14). [SSC MTS 04/09/2023 (1st Shift)]

17. Water is pouring into a cuboidal reservoir at the rate of 50 litres per minute. The volume of the reservoir is 120 m³. How many hours will it take to fill the reservoir ? [SSC MTS 04/09/2023 (3rd Shift)]

18. Using the middle points of sides of a square with an area of 36 square units, another square is made. What is the area of a new square made in square units? [SSC MTS 05/09/2023 (2nd Shift)]

19. The length of the median of an equilateral triangle is 6√3 cm. The area of the triangle is: [SSC MTS 05/09/2023 (3rd Shift)]

20. The areas of three adjacent faces 2 of a cuboid are p, q and r unit², respectively. What is its volume? [SSC MTS 06/09/2023 (3rd Shift)]

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