Question

A conical tent is to accommodate $77$ persons. Each person must have $16m^3$ of air to breathe. Given the radius of the tent as $7$m find the height of the tent and also its curved surface area.

Answer 1

Volume of air required for a person to breathe$=16m^3$

Volume of air required for $77$ persons to breathe $=77\times 16m^3=1232m^3$

Radius of the base of the tent $=7m$

Now,

Volume of the tent$=\frac{1}{3}\times \pi r^{2}h$

$\Rightarrow 1232m^3=\frac{1}{3}\times \frac{22}{7}\times 7^2\times h$

$\Rightarrow h=24m$

$\therefore$ Height of the tent $=24m$

Slant height $l=\sqrt{r^2+h^2}=\sqrt{7^2+{24}^2}=\sqrt{49+576}=\sqrt{625}=25m$

Now,

Curved Surface area$=\pi rl$

$=\frac{22}{7}\times 7\times 25$

$=550m$

$\therefore$ Curved surface area$=550m$