A conical tent has to accommodate 25 persons. Each person must have 4 m² of space on the ground and 80 m³ of air to breathe. Find the height of the tent.

Solution (By Examveda Team)

$$\eqalign{ & \pi {r^2} = 25 \times 4 \cr & \pi {r^2} = 100{\text{ }}{{\text{m}}^2} \cr & {r^2} = \frac{{100}}{\pi } \cr & {\text{Volume}} = \frac{1}{3}\pi {r^2}h \cr & 80 \times 25 = \frac{1}{3} \times \pi \times \frac{{100}}{\pi } \times h \cr & h = 60{\text{ m}} \cr} $$