If you are given a rectangular canvas of 1.5 m in width, what length of this canvas would you require to make a conical tent that is 48 m in diameter and 7 m in height? Note that 10% of the canvas is used (wasted) in folds and stitchings.
Also, find the cost of the canvas at the rate of ₹24 per meter.

Given,

Diameter of tent = 48 m

Radius (r) = $\dfrac{48}{2}$ = 24 m

Height (h) = 7 m

Slant height = l

We know that,

⇒ l² = h² + r²

⇒ l² = 7² + 24²

⇒ l² = 49 + 576

⇒ l² = 625

⇒ l = $\sqrt{625}$

⇒ l = 25 m.

Curved surface area = πrl

= $\dfrac{22}{7} \times 24 \times 25$

= 1885.71 m²

Given, 10% of canvas is used in folds and stitchings.

∴ $\dfrac{10}{100} \times 1885.71$ = 188.571 m².

Total area of canvas = 1885.71 + 188.571 = 2074.28 m².

By formula,

⇒ Area of canvas = Length of canvas × Breadth of canvas

⇒ 2074.28 = Length × 1.5

Length = $\dfrac{2074.28}{1.5}$ = 1382.85 m.

Given,

Cost of 1 m = ₹ 24

∴ Cost of 1382.85 m = 1382.85 × 24 = ₹ 33188.40.

Hence, length of canvas required = 1382.85 m and cost of canvas = ₹ 33188.40.