Question

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. Find the height of the cone.

Answer 1

Area of base = $11\times 4=44$ $m^2$

$\pi r^2=44$ $m^2$

Volume of the cone = $11\times 20=220$ $m^3$

$\frac{1}{3}\pi r^{2}h=220$ $m^3$

Therefore,

$\frac{\frac{1}{3}\pi r^{2}h}{\pi r^2}=\frac{220}{44}$

$\frac{h}{3}=5$

$h=15$ $m$