### Theory:

The volume of the solid formed by combining two more solids is obtained by simply calculating the volume of the individual solids and adding them.

Suppose a solid is in the form of a cone surmounted on a hemisphere, then its volume is given by the sum of the volume of the cone and the hemisphere.

Let us discuss an example to understand the concept better.
Example:
The interior of the glass is in the form of a cylinder surmounted on a hemisphere has a uniform radius of $$4$$ $$cm$$ and the height of the cylindrical part is $$7$$ $$cm$$. Find the capacity of the glass.

Solution:

The volume of the glass $$=$$ Volume of the hemisphere $$+$$ Volume of the cylinder

Volume of the glass $$=$$ $$\frac{2}{3} \pi r^3$$ $$+$$ $$\pi r^2 h$$

$$=$$  $$\left[\frac{2}{3} \times \frac{22}{7} \times (4)^3\right]$$ $$+$$ $$\left[\frac{22}{7} \times (4^2) \times 7 \right]$$

$$=$$  $$\left[\frac{2}{3} \times \frac{22}{7} \times 64\right]$$ $$+$$ $$\left[\frac{22}{7} \times 16 \times 7 \right]$$

$$=$$ $$134.1$$ $$+$$ $$352$$

$$=$$  $$486.1$$ $$cm^3$$

Therefore, the capacity of the glass is $$486.1$$ $$cm^3$$.