VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

31. If the ratio of the circumference of the base of a right circular cone of radius r to its height is 3 : 1, then what is the area of the curved surface of the cone? [2018 (I) Morning Shift]

Correct Answer: (d)
Solution:Let the radius of cone be ‘r’ and height be ‘h’

32. The surface area of a closed cylindrical box is 352 cm2 . If its height is 10 cm, then what is its diameter? (Use π = ²²⁄₇) [2018 (I) Morning Shift]

Correct Answer: (b) 8 cm
Solution:Let ‘r’ be radius of base of cylindrical box.

33. If the ratio of the radius of the base of a right circular cone to its slant height is 1 : 3, what is the ratio of the total surface area to the curved surface area? [2018 (I) Morning Shift]

Correct Answer: (d) 4 : 3
Solution:Ratio of the radius of base and slant height of cone = 1 : 3

34. What is the volume of a cone of maximum volume cut out from a cube of edge 2a such that their bases are on the same plane? [2018 (I) Morning Shift]

Correct Answer: (c)
Solution:

35. A hollow cube is formed by joining six identical squares. A rectangular cello tape of length 4 cm and breadth 0.5 cm is used for joining each pair of edges. What is the total area of cello tape used? [2017 (II) Evening Shift]

Correct Answer: (b) 24 cm²
Solution:There are 12 edges in a cube cello tape used for an edge is = 4 × 0.5 = 2cm²
∴ Total area of cello tape used = 12 × 2 = 24cm²

36. The cylinder of height 2x is the circumscribed by a sphere of radius 2x such that the circular ends of the cylinder are two small circles on the sphere. What is the ratio of the curved surface area of the cylinder to the surface area of the sphere? [2017 (II) Evening Shift]

Correct Answer: (a) √3 : 4
Solution:We have, height of cylinder= 2x


37. A cylindrical vessels 60 cm in diameter is partially filled with water. A sphere 30 cm in diameter is gently dropped into the vessel and is completely immersed. To what further height will the water in the cylinder rise? [2017 (II) Evening Shift]

Correct Answer: (d) 5 cm
Solution:Let h be the height of water in cylinder rise.

38. The vertical angle of a right circular cone is π/2 and the slant height is √2r cm. Where ‘r’ is the radius of cone What is the volume of the cone in cubic cm? [2017 (II) Evening Shift]

Correct Answer: (c) πr³
Solution:We have, vertical angle of cone = π/2


39. The radii of the frustum of a right circular cone are in the ratio 2 : 1. What is the ratio of the volume of the frustum of the cone to that to the whole cone? [2017 (II) Evening Shift]

Correct Answer: (d) 7 : 8
Solution:


40. From a solid cylinder whose height is 8 cm and of base radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is formed by hollowing out. What is the inner surface area of the cavity? [2017 (II) Evening Shift]

Correct Answer: (d) 60 π cm
Solution:We have, Height of cylinder = Height of cone = 8 cm