The circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it.

Given,

Circumference of base = 66 m

⇒ 2πr = 66

⇒ $2 \times \dfrac{22}{7} \times r = 66$

⇒ r = $\dfrac{66 \times 7}{2 \times 22} = \dfrac{21}{2}$ = 10.5 cm

By formula,

Volume of cone = $\dfrac{1}{3}πr^2h$

$= \dfrac{1}{3} \times \dfrac{22}{7} \times (10.5)^2 \times 12 \\[1em] = \dfrac{22 \times 110.25 \times 4}{7} \\[1em] = \dfrac{9702}{7} \\[1em] = 1386 \text{ m}^3.$

Hence, volume of air contained in cone = 1386 m³.