VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

41. A tent has been constructed which is in the form of right circular cylinder surmounted by a right circular cone whose axis coincides with the axis of the cylinder. If the radius of the base of the cylinder is 50 m, the height of the cylinder is 10 m and the total height of he tent is 15 m, then what is the capacity of the tent is cubic metres? [2017 (II) Evening Shift]

Correct Answer: (b) 87500π/3
Solution:We have, height of cylinder = 10 m


42. Two rectangular sheets of sizes of 2π × 4π and π × 5× are available. A hollow right circular cylinder can be formed by joining a pair of parallel sides of any sheet. What is the maximum possible volume of that circular cylinder that can be formed this way? [2017 (II) Evening Shift]

Correct Answer: (b) 8π²
Solution:We have,

43. A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe? [2017 (I) Morning Shift]

Correct Answer: (c) 8800 square cm
Solution:Diameter of the cylinder = Diameter of spherical ball = 2 cm

44. If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone? [2017 (I) Morning Shift]

Correct Answer: (d)
Solution:Let r and h be the original radius and height of the cone respectively.


45. If the surface area of a sphere is reduced to one ninth of the area, its radius reduces to [2017 (I) Morning Shift]

Correct Answer: (b) One-third
Solution:Let original and new radius of the sphere are r and r′ respectively.

46. Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is [2017 (I) Morning Shift]

Correct Answer: (c) 1050
Solution:Number of persons

47. (Questions 47-49) A tent of a circus is made of canvas and is in the form of right circular cylinder and right circular cone above it. The height and diameter of the cylindrical part of the tent are 5m and 126 m, respectively. The total height of the tent is 21 m. [2016 (II) Evening Shift]

What is the slant height of the cone?

Correct Answer: (b) 65 m
Solution:Given, height of tent = 21m and height of cylindrical part (h₁) = 5 m

48. What is the curved surface area of the cylinder? [2016 (II) Evening Shift]

Correct Answer: (a) 1980 m²
Solution:Curved surface area of the cylinder

= 2πrh₁
= 2 × 22/7 × 63 × 5 = 1980m²

49. How many square metres of canvas are used? [2016 (II) Evening Shift]

Correct Answer: (d) 14850
Solution:Total canvas used = Curved surface area of cylinder + Curved surface area of cone

50. A building is in the form of a cylinder surmounted by a hemispherical dome on the diameter of the cylinder. The height of the building is three times the radius of the base of the cylinder. The building contains 67¹⁄₂₈ of air. What is the height of the building? [2016 (II) Evening Shift]

Correct Answer: (a) 6 m
Solution:Let r be the radius of the cylinder.