The surface area of a solid metallic sphere is 1256 cm². It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate

(i) the radius of the solid sphere.

(ii) the number of cones recast. (Use π = 3.14).

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 the water in the can before the sphere was put into the can. Given your answer as proper fractions.

The radius of a roller 100 cm long is 14 cm. The curved surface area of the roller is

1. 13200 m²

2. 15400 m²

3. 4400 m²

4. 8800 m²

If two cylinders of the same lateral surface have their radii in the ratio 4 : 9, then the ratio of their heights is

1. 2 : 3

2. 3 : 2

3. 4 : 9

4. 9 : 4