Question

A conical tent is to accommodate 11 persons. Each person must have 4 square metres of the space on the ground and $20m^3$ of air to breathe. Find the height of the cone.

• A. 15 m
• B. 20 m
• C. 18 m
• D. 16 m

Answer 1

The correct option is A

15 m

Required area of the base of cone = $11\times 4=44m^2$
and required volume of cone $=11\times 20=220m^3$
$\Rightarrow \frac{1}{3}\left(\pi r^{2}h\right)=220\Rightarrow \frac{1}{3}\times 44\times h=220\Rightarrow h=\frac{220\times 3}{44}=15m$
$\therefore$ Height of cone = 15 m