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 ₹ 25 per metre.

Answer 1

We have,

Width of the cloth, B = 5 m,

Radius 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)`

`= sqrt(7^2 + 24^2)`

`= sqrt(49 + 576)`

`=sqrt(625)`

= 25 m

Now,

The curved surface of the conical tent = πrl

`=22/7xx7xx25`

⇒ The area of the cloth used for making the tent = 550 m² 

⇒ LB = 550

`=> "L" = 550/"B"`

`=> "L" = 550/5`

⇒ L = 110 m

So, the cost of the cloth used = 25 × 110 = ₹ 2750

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