The volume of the greatest sphere cut off from a circular cylindrical wood of base radius 1 cm and height 6 cm is

1. 288π cm³

2. $\dfrac{4}{3}π$ cm³

3. 6π cm³

4. 4π cm³

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

1. 3 : 4

2. 4 : 3

3. 9 : 16

4. 16 : 9

If a sphere and a cube have equal surface areas, then the ratio of the diameter of the sphere to the edge of the cube is

1. 1 : 2

2. 2 : 1

3. $\sqrt{π} : \sqrt{6}$

4. $\sqrt{6} : \sqrt{π}$

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

1. 21 cm

2. 23 cm

3. 25 cm

4. 19 cm