A conical tent is to accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breath. The height of the cone is :

Answer: Option C

Let the radius of base = r and height = h
Required floor area :
= (4 × 11) m² = 44 m²
Required volume :
= (20 × 11) m³ = 220 m³
So,
$$\begin{array}{rl}& \frac{1}{3}\pi r^{2}h=220\\ & \Rightarrow \frac{1}{3}\times 44\times h=220\\ & \Rightarrow h=\frac{220\times 3}{44}\\ & \Rightarrow h=15m\end{array}$$