Mathematics

How many metres of canvas 1.25 m will be needed to make a conical tent whose base radius is 17.5 m and height 6 m?

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Given, r = 17.5 m and h = 6 m

l² = r² + h²

⇒ l² = 17.5² + 6²

⇒ l² = 306.25 + 36

⇒ l² = 342.25

⇒ l = $\sqrt{342.25}$ = 18.5 m

So, the total curved surface area of the tent = πrl

$= \dfrac{22}{7} \times 17.5 \times 18.5 \\[1em] = \dfrac{7122.5}{7} \\[1em] = 1017.5 \text{ m}^2$

Width of the canvas used = 1.25 m

Length of canvas = $\dfrac{\text{area of canvas}}{\text{width of canvas}} = \dfrac{1017.5}{1.25}$ = 814 m.

Hence, 814 metres of canvas will be needed to make a conical tent.

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