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 :

Solution (By Examveda Team)

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,
$$\eqalign{ & \frac{1}{3}\pi {r^2}h = 220 \cr & \Rightarrow \frac{1}{3} \times 44 \times h = 220 \cr & \Rightarrow h = \frac{{220 \times 3}}{{44}} \cr & \Rightarrow h = 15\,m \cr} $$