71. A hollow spherical metallic ball has an external diameter 6 cm and is $$\frac{1}{2}$$ cm thick. The volume of metal used in the ball is :
72. If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cylinder of base diameter 8 cm, then the height of the cylinder is :
73. The ratio of the volume of a hemisphere and a cylinder circumscribing this hemisphere and having a common base is :
74. The volume of a right circular cone which is obtained from a wooden cube of edge 4.2 dm wasting minimum amount of wood is :
75. If the diameter of a sphere is 6 m, its hemisphere will have a volume of :
76. The length of the longest rod that can be placed in a room of dimensions 10 m × 10 m × 5 m is :
77. The sum of the radius and the height of a cylinder is 19 m. The total surface area of the cylinder is 1672 m2, what is the volume of the cylinder ?
78. Given that 1 cu. cm of marble weights 25 gms, the weight of a marble block 28 cm in width and 5 cm thick is 112 kg. The length of the block is :
79. An open box is made by cutting the congruent squares from the corners of a rectangular sheet of cardboard of dimension 20 cm × 15 cm. If the side of each square is 2 cm, the total outer surface area of the box is :
80. V1, V2, V3 and V4 are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4 cm respectively. Some statements regarding these volumes are given below :
(i) V1 + V2 + 2V3 < V4
(ii) V1 + 4V2 + V3 < V4
(iii) 2(V1 + V3) + V2 = V4
Which of these statements area correct ?
(i) V1 + V2 + 2V3 < V4
(ii) V1 + 4V2 + V3 < V4
(iii) 2(V1 + V3) + V2 = V4
Which of these statements area correct ?
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