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.

Answer 1

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.