VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

61. Consider the following statements. [2015 (II) Evening Shift]

1. If the height of a cylinder is doubled, the area of the curved surface is doubled.
2. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

Which of the above statement(s) is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:

62. A large water tank has the shape of a cube. If 128 m³. of water is pumped out, the water level goes down by 2m. Then, the maximum capacity of the tank is [2015 (II) Evening Shift]

Correct Answer: (a) 512 m³
Solution:Let the side of water tank be l m.

63. Simplify the question [2015 (II) Evening Shift]

Correct Answer: (c) 6
Solution:Let n spherical balls be made and r be the radius of each sphere.


64. 30 metallic cylinders of same size are melted and cast in the form of cones having the same radius and height as those of the cylinders. [2015 (II) Evening Shift]

Consider the following statements

Statement I A maximum of 90 cones will be obtained.
Statement II The curved surface of the cylinder can be flattened in the shape of a rectangle but the curved surface of the cone when flattened has the shape of triangle.

Which one of the following is correct in respect of the above?

Correct Answer: (b) Both Statements I and II are correct and Statement II is not the correct explanation of Statement I
Solution:Let radius be r and height be h of the cylinder.

65. A water tank, open at the top, is hemispherical at the bottom and cylindrical above it. The radius is 12 m and the capacity is 3312π m³. The ratio of the surface areas of the spherical and cylindrical portions, is [2015 (II) Evening Shift]

Correct Answer: (b) 4 : 5
Solution:Let the height of cylindrical part be h. Then, 2/3 πr³ + πr² h = 3312 π


66. The areas of three mutually perpendicular faces of a cube are x, y, z. If V is the volume, then xyz is equal to [2015 (II) Evening Shift]

Correct Answer: (b) V²
Solution:Let the sides of cube be l.

67. Let V be the volume of an inverted cone with vertex at origin and the axis of the cone is along positive Y-axis. The cone is filled with water up to half of its height. The volume of water is [2015 (II) Evening Shift]

Correct Answer: (a) V/8
Solution:


68. Three rectangles R₁, R₂ and R have the same area. Their lengths x₁, x₂ and x₃ respectively are such that x₁ < x₂ < x₃. If V₁ V₂ and V₃ are the volumes of the the 2 cylinders formed from the rectangles R₁, R₂ and R₃ respectively by joining the parallel sides along the breadth, then which one of the following is correct? [2015 (II) Evening Shift]

Correct Answer: (a)
Solution:Let the area be A.


69. If the surface area of a cube is 13254 cm² , then the length of its diagonal is [2015 (II) Evening Shift]

Correct Answer: (d) 47√3 cm
Solution:Let the sides of a cube be l cm.

70. How many spherical bullets each of 4 cm in diameter can be made out of a cube of lead whose edge is 44 cm? [2015 (II) Evening Shift]

Correct Answer: (a) 2541
Solution:Let n bullets be made.