Question

A solid is in the form of a right 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 the water left in the tub.

Answer 1

The object is shown in the figure below.

Radius of hemisphere = 2.1 cm
Volume of hemisphere$=\frac{2}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1=19.404{\mathrm{cm}}^3$

Height of cone = 4 cm
Volume of cone $=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 4=18.48{\mathrm{cm}}^3$
Volume of the object$=18.48+19.404=37.884c{m}^3$

Volume of cylindrical tub$={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 5\times 5\times 9.8=770{\mathrm{cm}}^3$

When the object is immersed in the tub, volume of water equal to the volume of the object is displaced from the tub.

Volume of water left in the tub = $770-37.884=732.116c{m}^3$