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Question
Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitchings. Also, find the cost of the canvas at the rate of Rs. 24 per metre.
Solution
Diameter of the tent = 48 m
Therefore, radius (r) = 24 m
Height (h) = 7 m
Slant height (ℓ) = `sqrt(r^2 + h^2)`
= `sqrt((24)^2 + (7)^2)`
= `sqrt(576 + 49)`
= `sqrt(625)`
= 25 m
Curved surface area = `pirl`
= `22/7xx24xx25`
= `13200/7 m^2`
= 1885.71 m2
But it is given that 10% allowance for folds and stitching
Hence modified area = `1885.71 m^2 + 10/100 xx 1885.71 m^2`
= 2074.28 m2
Width of canvas = 1.5 m
∴ Length of canvas = `"Area of canvas"/"Width of canvas"`
= `(2074.28 m^2)/(1.5 m)`
= 1382.85 m
Now cost of 1 m = Rs. 24
Hence cost of 1382.85 m = Rs. 24 × 1382.85 = Rs. 33188.4.
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