# Mensuration-57

### From Homeworkwiki

**A solid is in the form of a circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm**

**and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water, in such a way that the**

**whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm.**

**find the volume of water left in the cylindrical tub.**

**Solution:** Height of the cylinder = H = 9.8 cm

Radius of cylindrical tub = R = 5 cm

Volume of water in cylindrical tub = Π R^{2} H

= (Π x 5 x 5 x 9.8) cm^{2}

= (22/7 x 25 x 98/10) cm^{2}

Radius of hemisphere = Radius of cone = r = 2.1 cm

Height of conical portion = 4 cm

Therefore, Volume of solid = Volume of hemisphere + Volume of cone

= 2/3 Π r^{3} + 1/3 Π r^{2} h = 1/3 Π r^{2} (2r + h)

= 1/3 x 22/7 x 21/10 x 21/10 (2 x 2.1 + 4) cm^{3} = 1/3 x 22/7 x 21/10 x 21/10 x 82/10 cm^{3}

= 37.884 cm^{3}

Therefore, Volume of water left = (770 - 37.884) cm^{3} = 732.166 cm^{3}