A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm is molded to form a solid sphere. Radius of the sphere is:

(a) 25 cm                            (b) 21 cm

(c) 19 cm                            (d) 23 cm

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:

(a) 3 : 2 : 1

(b) 1 : 3 : 2

(c) 2 : 3 : 1

(d) 1 : 2 : 3

A garden roller has a circumference of 4 m. The no. of revolutions it makes in moving 40 metres are:

(a) 12                                  (b) 16

(c) 8                                     (d) 10

The ratio of volume of a cone and a cylinder of equal diameter and equal height is:

(a) 3 : 1

(b) 1 : 3

(c) 1 : 2

(d) 2 : 1

If a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere, then the radius of the sphere is:

(a) 6 cm                              (b) 4 cm

(c) 8 cm                              (d) 12 cm

A solid sphere of diameter 6 cm is melted and drawn into a wire of radius 4 mm. The length of wire is:

(a) 900 cm                         (b) 90 cm

(c) 900 m                            (d) 225 cm

If a cone is cut into two parts by a horizontal plane passing through the mid-points of its axis, the ratio of the volumes of the upper part and the cone is:

(a) 1 : 2

(b) 1 : 4

(c) 1 : 6

(d) 1 : 8

The volume of a sphere (in cu. cm) is equal to its surface area (in sq. cm). The diameter of the sphere (in cm) is:

(a) 3                                     (b) 6

(c) 2                                     (d) 4

A child reshapes a cone made up of China clay of height 24 cm and radius of base 6 cm into a sphere. The radius of the sphere is:

(a) 24 cm                            (b) 12 cm

(c) 6 cm                              (d) 48 cm

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is:

(a) \(60 \pi cm^2\)

(b) \(68 \pi cm^2\)

(c) \(120 \pi cm^2\)

(d) \(136 \pi cm^2\)