A vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result one-fourth of water in the original cone overflows. What is the volume of each of the solid cones submerged?

The volume of a conical tent is 1232 m³ and the area of the base floor is 154 m². Calculate the :

(i) radius of the floor,

(ii) height of the tent,

(iii) length of the canvas required to cover this conical tent if its width is 2 m.

A hemi-spherical bowl (as shown) has external radius R and internal radius r, the outer surface area of the bowl is :

1. 2πR² + πr²

2. 3πR² - πr²

3. 2πR² + 2πr²

4. 2πR² - πr²

The ratio between the volumes of two spherical solids is 27 : 8. The ratio between their curved surface areas is :

1. 27 : 8

2. 8 : 27

3. 3 : 2

4. 9 : 4