Question

The volume of a conical tent is 1232 $m^3$ and the area of the base floor is 154 $m^2$. Calculate the :

(i) radius of the floor,

(ii) height of the tent,

(iii) length of the canvas required to cover this conical tent if its width is 2 m.

Answer 1

The volume of the conical tent = $\frac{1}{3}\times \frac{22}{7}\times r^2\times h$ = 1232 $m^3$

= $\frac{22}{7}\times r^2\times h$ = 3696 $m^3$

Area of the base floor = $\frac{22}{7}\times r^2$ = 154 $m^2$

$r^2$ = $\frac{154\times 7}{22}$ = 49

r = 7 m

$\frac{22}{7}\times r^2\times h$ = 3696 $m^3$

$154\times h$ = 3696 $m^3$

h = $\frac{3696}{154}$ = 24 m

Curved surface area of the tent = $\frac{22}{7}\times r\times l$

= $\frac{22}{7}\times 7\times \sqrt{7^2+{24}^2}$

= $22\times \sqrt{49+576}$

= $22\times 25$ = 550 $m^2$

so 550 $m^2$ canvas is required to make the tent.
area of canvas = 550 $m^2$

length of canvas = $\frac{550}{2}$ = 275 m.