How many metres of cloth 2.5 m wide will be required to make a conical tent whose base radius is 7 m and height is 24 m?

1. 120 m

2. 180 m

3. 220 m

4. 550 m

Given, r = 7 m and h = 24 m

l² = r² + h²

⇒ l² = 7² + 24²

⇒ l² = 49 + 576

⇒ l² = 625

⇒ l = $\sqrt{625}$ = 25 m

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

$= \dfrac{22}{7} \times 7 \times 25 \\[1em] = 22 \times 25 \\[1em] = 550 \text{ m}^2$

Width of the cloth used = 2.5 m

Length of canvas = $\dfrac{\text{area of canvas}}{\text{width of canvas}} = \dfrac{550}{2.5}$ = 220 m.

Hence, option 3 is the correct option.