How many meters of cloth 6 metre wide will be required to make a conical tent, the radius of whose base is 21m and height is 20m?

319 metre

The correct answer is Option (4) → 319 metre

First find the slant height of the conical tent:

$l = \sqrt{r^2 + h^2} = \sqrt{21^2 + 20^2} = \sqrt{441 + 400} = \sqrt{841} = 29 \text{ m}$

Now calculate the curved surface area of the cone:

$\text{CSA} = \pi r l = \pi \times 21 \times 29 = 609\pi \text{ m}^2$

Since the cloth is 6 m wide, the length of cloth required is:

$\frac{609\pi}{6} = 101.5\pi \approx 319 \text{ m}$