A cylindrical can, whose base is horizontal and of radius 3.5 cm, contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate :

(i) the total surface area of the can in contact with water when the sphere is in it;

(ii) the depth of water in the can before the sphere was put into the can.

A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is 10 cm when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is 7 cm and height of cylinder is 20 cm.

The radii of two solid spheres are 10 cm and 20 cm. The ratio between their volumes is :

1. 3 : 8

2. 1 : 4

3. 1 : 8

4. 8 : 3

A cone and a sphere have equal volumes. If height of the cone = radius of the sphere = 10 cm, the radius of the cone is :

1. 40 cm

2. 10 cm

3. 30 cm

4. 20 cm