Question

Choose the correct answer in each of the following :

A conical tent is to accommodate 11 persons such that each person occupies $4m^2$ of space on the ground.They have $220m^3$ of air to breathe. The height of the cone is

(a) 14 m (b) 15 m (c) 16 m (d) 20 m

Answer 1

Ans-b

As each person needs 4 sq.m space on ground
So 11 person will need 44 sq.m space on the ground.
Therefore,
Area of ground = 44sq.m
$\pi r^2=44sq.m$
$r^2=\frac{44}{\pi }$ .......(1)
and each person needs 20 cu.m of air
So 11 persons will need 220 cu .m of air
Therefore volume of tent = 220 cu.m
$\frac{1}{3}\pi r^{2}h=220cu.m$
$\frac{1}{3}\times 44\times h=220$
$h=\frac{220\times 3}{44}$
$h=5\times 3$
$h=15cm$