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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.
Solution
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.
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