Question

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of Rs 25 per metre.

Answer 1

We have,

Width of the cloth, B = 5 m,

Radius of the conical tent, r = $\frac{14}{2}$ = 7 m and

Height of the conical tent, h = 24 m

Let the length of the cloth used for making the tent be l.

Also,

The slant height of the conical tent,
l = $\sqrt{r^2+h^2}$

l = $\sqrt{7^2+{24}^2}$

l = $\sqrt{49+576}$

l = $\sqrt{625}$

l = 25 m

Now,

The curved surface of the conical tent = πrl

= $\frac{22}{7}$×7×25 = 550 $m^2$

The area of the cloth used for making the tent is 550 $m^2$

Area of cloth used = curved surface area of the conical tent

⇒ LB = 550

⇒ L = $\frac{550}{B}$

⇒ L = $\frac{550}{5}$

⇒ L = 110 m

So, the cost of the cloth used = 25 x 110 = 2750

So, the cost of the cloth used for making the tent is Rs. 2750.