A circus tent is in the form of a cylinder surmounted by a cone. The radius of the base of the cylinder is 30 feet and its height is 10 feet. If the total height of the tent is 20 feet, then the volume of the air (in cubic feet) in the tent is

Given, the circus tent is in the form of a cylinder surmounted by a cone.

The circus is in the shape of cone placed over cylinder. Radius of both will be equal.

Radius of the cylinder = 30 feet

$$\Rightarrow$$ Radius of the cone = 30 feet

Height of the cylinder = 10 feet

Total height of the tent = 20 feet

$$\Rightarrow$$ Height of the cone = 20 - 10 = 10 feet

$$\therefore\ $$Volume of the tent = Volume of the cylinder + Volume of the cone

$$=\pi\ \left(30\right)^2\left(10\right)+\frac{1}{3}\pi\left(30\right)^2\left(10\right)$$

$$=\frac{4}{3}\pi\left(30\right)^2\left(10\right)$$

$$=\frac{4}{3}\pi\times9000$$

$$=12000\pi$$ cubic feet

Hence, the correct answer is Option C