Question

A conical tent was erected by army at a base camp with height $3\text{m}$ and base diameter $8\text{m}$. Find :
(i) The cost of canvas required for making the tent, if the canvas cost $\text{Rs.}70$ per $1\text{sq. m}$.
(ii) If every person requires $3.5$ ${\text{m}}^2$ air, how many persons can be seated in that tent.

Answer 1

Diameter of the tent $=8\text{m}$
$r=\frac{d}{2}=\frac{8}{2}=4\text{m}$
Height $=3\text{m}$
Slant height $\left(l\right)=\sqrt{h^2+r^2}$
$=\sqrt{3^2+4^2}$
$=\sqrt{25}=5\text{m}$
Therefore, curved surface area of tent $=\pi rl$
$=\frac{22}{7}\times 4\times 5=\frac{440}{7}{\text{m}}^2$
Volume of the cone $=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times 4\times 4\times 3$
$=\frac{352}{7}{\text{m}}^3$

(i) Cost of canvas required for the tent
$=$ C.S.A. $\times$ Unit cost
$=\frac{440}{7}\times 70$
$=$ $\text{Rs.}4400$

(ii) Number of persons can be seated in the tent
$=\frac{\text{Volume of conical tent}}{\text{Air required for each}}$
$=\frac{352}{7}÷3.5$
$=\frac{352}{7}\times \frac{1}{3.5}=14.36$
$=14$ men (approx.)