Mensuration (Part-7)

41. The diameter of a hemispherical bowl is 21 cm. The volume of the bowl is equal to: (Use π = 22/7) [SSC CHSL Tier II (02/11/2023)]

(a) 2,624.5 cm³
(b) 2,425.5 cm³
(c) 2,725.5 cm³
(d) 2,524.5 cm³

Correct Answer: (b) 2,425.5 cm³

Solution:

42. The radius and height of a right circular cone is increased by 25%. Find the increase in percentage of the volume of the cone (rounded off to 2 decimal places). [SSC CHSL Tier II (02/11/2023)]

(a) 94.31%
(b) 95.31%
(c) 94.51%
(d) 93.51%

Correct Answer: (b) 95.31%

Solution:

43. A hollow cube is made of paper to have a volume of 512 cubic units. How much paper in square units will be required to make the cube? [SSC CHSL Tier II (10/01/2024)]

(a) 328
(b) 348
(c) 288
(d) 384

Correct Answer: (d) 384

Solution:

44. A box's right rectangular measurements are 1.6 m long, 90 cm wide, 60 cm in height. Soap cakes of measurement 6 cm x 5 cm x 40 mm are to be packed in the box, so that no space is left. How many cakes can be packed in the box? [SSC CHSL Tier II (10/01/2024)]

(a) 6000
(b) 5600
(c) 6500
(d) 7200

Correct Answer: (d) 7200

Solution:

45. The ratio of the length, width and height of a closed cuboid is given as 6:3:2. The total surface area of this cuboid is given as 1800 cm². Find the volume (in cm³) of this cuboid. [SSC CGL Tier II (26/10/2023)]

(a) 4650
(b) 4800
(c) 4500
(d) 4200

Correct Answer: (c) 4500

Solution:

46. A solid cube, whose each edge is of length 48 cm, is melted. Identical solid cubes, each of volume 64 cm³, are made out of this molten cube, without any wastage. How many such small cubes are obtained ? [SSC CGL Tier II (26/10/2023)]

(a) 1728
(b) 1718
(c) 1748
(d) 1738

Correct Answer: (a) 1728

Solution:

47. The cost of painting the total surface area of a 30 m high solid right circular cylinder at the rate of ₹25 per m² is 18,425. What is the volume (in m³) of this cylinder [Use π = 22/7] [SSC CPO 03/10/2023 (2nd Shift)]

(a) 1210
(b) 1155
(c) 1145
(d) 1122

Correct Answer: (b) 1155

Solution:

48. What will be the difference between the total surface area and the curved surface area of a hemisphere having 4 cm diameter ? [SSC CPO 03/10/2023 (2nd Shift)]

(a) 4.4π cm²
(b) 5π cm²
(c) 4π cm²
(d) 8π cm²

Correct Answer: (c) 4π cm²

Solution:

49. A conical shape vessel has a radius of 21 cm and has a slant height of 25 cm. If the curved part of the vessel is to be painted white, find the cost (in ₹) of painting at the rate of ₹1.5 per cm². [SSC CPO 03/10/2023 (2nd Shift)]

(a) 2475
(b) 825
(c) 1650
(d) 1250

Correct Answer: (a) 2475

Solution:

50. A solid sphere made of wax of radius 12 cm is melted and cast into solid hemispheres of radius 4 cm each. Find the number of such solid hemispheres. [SSC CPO 03/10/2023 (3rd Shift)]

(a) 14
(b) 54
(c) 28
(d) 27

Correct Answer: (b) 54

Solution:

Mensuration (Part-7)

41. The diameter of a hemispherical bowl is 21 cm. The volume of the bowl is equal to: (Use π = 22/7) [SSC CHSL Tier II (02/11/2023)]

42. The radius and height of a right circular cone is increased by 25%. Find the increase in percentage of the volume of the cone (rounded off to 2 decimal places). [SSC CHSL Tier II (02/11/2023)]

43. A hollow cube is made of paper to have a volume of 512 cubic units. How much paper in square units will be required to make the cube? [SSC CHSL Tier II (10/01/2024)]

44. A box's right rectangular measurements are 1.6 m long, 90 cm wide, 60 cm in height. Soap cakes of measurement 6 cm x 5 cm x 40 mm are to be packed in the box, so that no space is left. How many cakes can be packed in the box? [SSC CHSL Tier II (10/01/2024)]

45. The ratio of the length, width and height of a closed cuboid is given as 6:3:2. The total surface area of this cuboid is given as 1800 cm². Find the volume (in cm³) of this cuboid. [SSC CGL Tier II (26/10/2023)]

46. A solid cube, whose each edge is of length 48 cm, is melted. Identical solid cubes, each of volume 64 cm³, are made out of this molten cube, without any wastage. How many such small cubes are obtained ? [SSC CGL Tier II (26/10/2023)]

47. The cost of painting the total surface area of a 30 m high solid right circular cylinder at the rate of ₹25 per m² is 18,425. What is the volume (in m³) of this cylinder [Use π = 22/7] [SSC CPO 03/10/2023 (2nd Shift)]

48. What will be the difference between the total surface area and the curved surface area of a hemisphere having 4 cm diameter ? [SSC CPO 03/10/2023 (2nd Shift)]

49. A conical shape vessel has a radius of 21 cm and has a slant height of 25 cm. If the curved part of the vessel is to be painted white, find the cost (in ₹) of painting at the rate of ₹1.5 per cm². [SSC CPO 03/10/2023 (2nd Shift)]

50. A solid sphere made of wax of radius 12 cm is melted and cast into solid hemispheres of radius 4 cm each. Find the number of such solid hemispheres. [SSC CPO 03/10/2023 (3rd Shift)]

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