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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,
the height of the cone, h = 24 m, the base diameter of the cone, `r = d/2 = 14/2 = 7 m`
Also, the base radius of the cone, `l = sqrt(h^2 + r^2)`
`= sqrt(24^2 + 7^2)`
`= sqrt(576 + 49)`
`=sqrt(625)`
`=25 m`
The curved surface area of the tent = `pirl`
`= 22/7xx 7xx25`
= 550 m2
⇒ The area of cloth requried to make the tent = 550 m2
⇒ The length of the cloth = `550/5 = 110 m`
So, the cost of cloth used = 110 ×25 = ₹2750
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