Mensuration (Part-6)

31. The base of a parallelogram is twice its height. If the area of the parallelogram is 338cm², then find its height (in cm) [SSC CPO 27/06/2024 (1st Shift)]

(a) 13
(b) 11
(c) 14
(d) 12

Correct Answer: (a) 13

Solution:

32. What is the total surface area of a cone whose radius is r/4 and slant height is 4ℓ? [SSC CPO 27/06/2024 (1st Shift)]

Correct Answer: (b)

Solution:

33. How many metres of cloth will be required to make a conical tent, the radius of whose base is 21 metres and height is 28 metres. The width of the cloth is 5 metres. (Where π = 22/7) [SSC CPO 27/06/2024 (1st Shift)]

(a) 470
(b) 462
(c) 456
(d) 478

Correct Answer: (b) 462

Solution:

34. The volume of a cube is four times the volume of a cuboid. If the sides of the cuboid are 32 cm, 8 cm and 4 cm, then find the ratio of the total surface area of the cube to that of the cuboid. [SSC CPO 27/06/2024 (2nd Shift)]

(a) 23:13
(b) 24:13
(c) 21:13
(d) 22:13

Correct Answer: (b) 24:13

Solution:

35. A copper sphere of diameter 12 cm is drawn into a wire of diameter 4 mm. What is the length (in cm) of the 22 wire? (Where π = 22/7) [SSC CPO 27/06/2024 (2nd Shift)]

(a) 7200
(b) 7823
(c) 8342
(d) 9000

Correct Answer: (a) 7200

Solution:

36. The length of the largest possible rod that can be placed in a cubical room is 42√3 m. The surface area (in m²) of the largest possible sphere that fit within the cubical room is: [Use π = 22/7] [SSC CPO 27/06/2024 (2nd Shift)]

(a) 3590
(b) 4589
(c) 2564
(d) 5544

Correct Answer: (d) 5544

Solution:

37. Find the area of a minor sector of a circle whose circumference is 88 cm and the length of its minor arc is 22 cm (use π = 22/7) [SSC CPO 27/06/2024 (2nd Shift)]

(a) 154 cm²
(b) 451 cm²
(c) 415 cm²
(d) 145 cm²

Correct Answer: (a) 154 cm²

Solution:

38. A rectangular sheet of metal is 60 cm by 25 cm. Equal squares of side 5 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. Find the volume of the box. [SSC CPO 27/06/2024 (3rd Shift)]

(a) 2750 cm³
(b) 5750 cm³
(c) 3750 cm³
(d) 4750 cm³

Correct Answer: (c) 3750 cm³

Solution:

39. A drainage tile is a cylindrical shell 42 cm long. The inside and outside diameters are 8 cm and 14 cm, respectively. What is the volume (in cm³) of clay required for the tile? (Use π = 22/7) [SSC CPO 27/06/2024 (3rd Shift)]

(a) 5241
(b) 4356
(c) 4881
(d) 4125

Correct Answer: (b) 4356

Solution:

40. One laddoo with a radius of 5 cm belongs to a shopkeeper. How many laddoos of radius 2.5 cm may be created from the same one laddoo? [SSC CPO 28/06/2024 (1st Shift)]

(a) 2
(b) 6
(c) 4
(d) 8

Correct Answer: (d) 8

Solution:

Mensuration (Part-6)

31. The base of a parallelogram is twice its height. If the area of the parallelogram is 338cm², then find its height (in cm) [SSC CPO 27/06/2024 (1st Shift)]

32. What is the total surface area of a cone whose radius is r/4 and slant height is 4ℓ? [SSC CPO 27/06/2024 (1st Shift)]

33. How many metres of cloth will be required to make a conical tent, the radius of whose base is 21 metres and height is 28 metres. The width of the cloth is 5 metres. (Where π = 22/7) [SSC CPO 27/06/2024 (1st Shift)]

34. The volume of a cube is four times the volume of a cuboid. If the sides of the cuboid are 32 cm, 8 cm and 4 cm, then find the ratio of the total surface area of the cube to that of the cuboid. [SSC CPO 27/06/2024 (2nd Shift)]

35. A copper sphere of diameter 12 cm is drawn into a wire of diameter 4 mm. What is the length (in cm) of the 22 wire? (Where π = 22/7) [SSC CPO 27/06/2024 (2nd Shift)]

36. The length of the largest possible rod that can be placed in a cubical room is 42√3 m. The surface area (in m²) of the largest possible sphere that fit within the cubical room is: [Use π = 22/7] [SSC CPO 27/06/2024 (2nd Shift)]

37. Find the area of a minor sector of a circle whose circumference is 88 cm and the length of its minor arc is 22 cm (use π = 22/7) [SSC CPO 27/06/2024 (2nd Shift)]

38. A rectangular sheet of metal is 60 cm by 25 cm. Equal squares of side 5 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. Find the volume of the box. [SSC CPO 27/06/2024 (3rd Shift)]

39. A drainage tile is a cylindrical shell 42 cm long. The inside and outside diameters are 8 cm and 14 cm, respectively. What is the volume (in cm³) of clay required for the tile? (Use π = 22/7) [SSC CPO 27/06/2024 (3rd Shift)]

40. One laddoo with a radius of 5 cm belongs to a shopkeeper. How many laddoos of radius 2.5 cm may be created from the same one laddoo? [SSC CPO 28/06/2024 (1st Shift)]

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