Mensuration (Part-6)

41. The cost of painting a spherical vessel of diameter 14 cm is ₹21,560. What is the cost of painting (in) per 22 square centimetre ? (Use π = 22/7) [SSC CPO 28/06/2024 (1st Shift)]

(a) 30
(b) 32
(c) 28
(d) 35

Correct Answer: (d) 35

Solution:

42. The radius of the base and height of a cone are 5 cm and 6 cm, respectively, whereas the radius of the base and height of a cylinder are 2.5 cm and 3 cm, respectively. The ratio of the volume of the cone to that of the cylinder is: (Where π = 22/7) [SSC CPO 28/06/2024 (1st Shift)]

(a) 8:5
(b) 9:4
(c) 8:3
(d) 3:5

Correct Answer: (c) 8:3

Solution:

43. A cylinder of radius 7 cm has a curved surface area of 2200cm². Find its total surface area. (Use π = 22/7) [SSC CPO 28/06/2024 (2nd Shift)]

(a) 2508 cm²
(b) 2260 cm²
(c) 2550 cm²
(d) 1580 cm²

Correct Answer: (a) 2508 cm²

Solution:

44. A hollow sphere of external and internal diameters of 10 cm and 6 cm, respectively, is melted and made into another solid in the shape of a right circular cone of base diameter 10 cm. Find the height of the cone. [SSC CPO 28/06/2024 (2nd Shift)]

(a) 13.68 cm
(b) 14.68 cm
(c) 16.68 cm
(d) 15.68 cm

Correct Answer: (d) 15.68 cm

Solution:

45. A spherical box has a surface area 528 cm². Find the radius of the spherical box. [SSC CPO 28/06/2024 (2nd Shift)]

(a) √37
(b) √42
(c) √29
(d) √35

Correct Answer: (b) √42

Solution:

46. The distance between the parallel sides of a trapezium is 18 cm. If the area of the trapezium is 1188 cm², then what is the sum of the lengths of the parallel sides? [SSC CPO 28/06/2024 (3rd Shift)]

(a) 150 cm
(b) 115 cm
(c) 126 cm
(d) 132 cm

Correct Answer: (d) 132 cm

Solution:

47. The area of the canvas cloth needed to erect a right conical tent of height 20ft. and circular base of circumference 30π ft. is: [SSC CPO 28/06/2024 (3rd Shift)]

(a) 455π sq.ft.
(b) 375π sq.ft.
(c) 589π sq.ft.
(d) 470π sq.ft.

Correct Answer: (b) 375π sq.ft.

Solution:

48. The volume of a right circular cone is 150π cm³ and its height is 18 cm. Find its slant height (in cm) (correct to 2 decimal places). [SSC CPO 28/06/2024 (3rd Shift)]

(a) 18.68
(b) 25.35
(c) 28.68
(d) 15.25

Correct Answer: (a) 18.68

Solution:

49. A school has two rectangular playgrounds, which are similar in shape. If the length and the breadth of the first playground are given as 224 m and 160 m, respectively, then which of the following options CANNOT be the dimensions of the second playground? [SSC CPO 29/06/2024 (1st Shift)]

(a) Length = 273 m; Breadth = 195 m
(b) Length = 168 m; Breadth = 120 m
(c) Length = 210 m; Breadth = 150 m
(d) Length = 343 m; Breadth = 255 m

Correct Answer: (d) Length = 343 m; Breadth = 255 m

Solution:

50. The height and radius of a cone-shaped storage tank are 9 ft. and 7 ft., respectively. Find the volume of water the tank can hold ? (Use π = 22/7) [SSC CPO 29/06/2024 (1st Shift)]

(a) 462 cubic ft.
(b) 527 cubic ft.
(c) 1386 cubic ft.
(d) 1423 cubic ft.

Correct Answer: (a) 462 cubic ft.

Solution:

Mensuration (Part-6)

41. The cost of painting a spherical vessel of diameter 14 cm is ₹21,560. What is the cost of painting (in) per 22 square centimetre ? (Use π = 22/7) [SSC CPO 28/06/2024 (1st Shift)]

42. The radius of the base and height of a cone are 5 cm and 6 cm, respectively, whereas the radius of the base and height of a cylinder are 2.5 cm and 3 cm, respectively. The ratio of the volume of the cone to that of the cylinder is: (Where π = 22/7) [SSC CPO 28/06/2024 (1st Shift)]

43. A cylinder of radius 7 cm has a curved surface area of 2200cm². Find its total surface area. (Use π = 22/7) [SSC CPO 28/06/2024 (2nd Shift)]

44. A hollow sphere of external and internal diameters of 10 cm and 6 cm, respectively, is melted and made into another solid in the shape of a right circular cone of base diameter 10 cm. Find the height of the cone. [SSC CPO 28/06/2024 (2nd Shift)]

45. A spherical box has a surface area 528 cm². Find the radius of the spherical box. [SSC CPO 28/06/2024 (2nd Shift)]

46. The distance between the parallel sides of a trapezium is 18 cm. If the area of the trapezium is 1188 cm², then what is the sum of the lengths of the parallel sides? [SSC CPO 28/06/2024 (3rd Shift)]

47. The area of the canvas cloth needed to erect a right conical tent of height 20ft. and circular base of circumference 30π ft. is: [SSC CPO 28/06/2024 (3rd Shift)]

48. The volume of a right circular cone is 150π cm³ and its height is 18 cm. Find its slant height (in cm) (correct to 2 decimal places). [SSC CPO 28/06/2024 (3rd Shift)]

49. A school has two rectangular playgrounds, which are similar in shape. If the length and the breadth of the first playground are given as 224 m and 160 m, respectively, then which of the following options CANNOT be the dimensions of the second playground? [SSC CPO 29/06/2024 (1st Shift)]

50. The height and radius of a cone-shaped storage tank are 9 ft. and 7 ft., respectively. Find the volume of water the tank can hold ? (Use π = 22/7) [SSC CPO 29/06/2024 (1st Shift)]

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