Theory:

In our day-to-day life, we come across a wide range of objects in the form of a combination of two or more solid shapes.

Let us discuss some real-life examples in this article where we can find the combination of one or more solids and learn how to find their volumes.

1. Capsule

The capsule is a combination of two solids, cylinder and hemisphere.

2. Circus tent

The circus tent is a combination of a cone and a cylinder.

3. Lollipop

The lollipop is a combination of a sphere and a cylinder.

Example:
The glass 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 $$486.1$$ $$cm^3$$.