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.

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& \pi r^2=25\times 4\\ & \pi r^2=100{\text{m}}^2\\ & r^2=\frac{100}{\pi }\\ & \text{Volume}=\frac{1}{3}\pi r^{2}h\\ & 80\times 25=\frac{1}{3}\times \pi \times \frac{100}{\pi }\times h\\ & h=60\text{ m}\end{array}$$