Find the length of canvas, 1.5m in width, is required to make a conical tent 14 m in diameter and 24 m in height. Given that `8(1)/(3)%` of the canvas is used in folds and stiching. Also, find the cost of canvas at the rate of Rs. 28 per metre.

Explanation

For conical tent,
r = 7 m, h = 24 m
`therefore l^(2)=h^(2)+r^(2)=24^(2)+7^(2)=25^(2)` (by Pythagoras theorem)
`rArr l = 25 m`
`therefore` curved surface area of tent `= pi rl`
`= (22)/(7)xx7xx25=550 m^(2)`
We have to take extra cloth for the canvas (for folding and stiching).
`therefore 1.5x-1.5x xx(25)/(3xx100)=550`
`therefore 450x-37.5x=165000`
`rArr 412.5x=165000 rArr x=400 m`
`therefore` Cost at the rate of Rs. 28 per metre `= Rs. 28xx400=Rs. 11200`