VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

91. If the side of a cube is increased by 100%, then by what percentage is the surface area of the cube increased? [2014 (II) Evening Shift]

Correct Answer: (c) 300%
Solution:Let side of a cube be x. Then, surface area of cube = 6x²

92. Consider the following statements in respect of four spheres A, B C, and D having respective radii 6, 8, 10 and 12 cm. [2014 (II) Evening Shift]

1. The surface area of sphere C is equal to the sum of surface areas of spheres A and B.
2. The volume of sphere D is equal to the sum of volumes of spheres A, B and C.

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

Correct Answer: (c) Both 1 and 2
Solution:1. Given, radius of sphere A = 6 cm, Radius of sphere B = 8 cm, Radius of sphere C = 10 cm and Radius of sphere D = 12 cm


93. What is the number of pairs of perpendicular planes in a cuboid? [2014 (II) Evening Shift]

Correct Answer: (c) 12
Solution:In a cuboid, 4 perpendicular face pairs in bottom surface, 4 perpendicular face pairs in top surface and 4 perpendicular face pairs in vertical surface. Hence, total perpendicular pairs are 12.

94. How many equilateral triangles can be formed by joining any three vertices of a cube? [2014 (II) Evening Shift]

Correct Answer: (c) 8
Solution:We know that, there are six faces in a cube. Let the sides of a cube be a


95. The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, then what is its radius equal to? [2014 (II) Evening Shift]

Correct Answer: (a) 0.1 cm
Solution:Given, diameter of a sphere, d = 6 cm

96. The volume of a hollow cube is 216 x³. What surface area of the largest sphere which can be enclosed in it? [2014 (I) Morning Shift]

Correct Answer: (c) 36π x²
Solution:∵ Volume of cube = 216 x³

97. What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 square cm? [2014 (I) Morning Shift]

Correct Answer: (a) 14 cm
Solution:∵ Surface area of sphere = 616 cm².

98. The dimensions of a field are 15 m by 12 m. A pit 8 m long, 2.5 m wide and 2 m deep is dug in one corner of the field and the earth removed is evenly spread over the remaining area of the field. The level of the field is raised by [2014 (I) Morning Shift]

Correct Answer: (c) 25 cm
Solution:Volume of earth dug out = 8 × 2.5 × 2 = 40m³

99. If 64 identical small spheres are made out of big sphere of diameter 8 cm, then what is surface area of each small sphere? [2014 (I) Morning Shift]

Correct Answer: (c) 4π cm²
Solution:Volume of each small sphere

100. A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone? [2014 (I) Morning Shift]

Correct Answer: (b) 8 : 1
Solution:Let the cone is divided into two parts by a line l.