Find the length of cloth used in making a conical pandal of height $$100$$m and base radius $$240$$m, if the cloth is $$100\pi$$ m wide.
Correct option is A. $$624$$ m.
Here,$$h=100\,m$$ and $$r=240\,m$$.
We know,
$$l=\sqrt{r^2+h^2}$$
$$l=\sqrt{240^2+100^2}$$
$$l=\sqrt{57600+10000}$$
$$l=\sqrt{67600}$$
$$l=260\,m$$.
Curved surface area $$=\pi r l$$
$$=\pi \times 240\times 260$$
$$=62400\pi\,m^2$$.
We know, Area of rectangle $$=$$ length $$\times$$ breadth.
$$\therefore$$ Length of the canvas required
$$=\dfrac{\text{Area of the cloth}}{\text{Width of the cloth}}$$ $$=\dfrac{62400\pi}{100\pi}$$ $$=624\,m$$.
Hence, the length of the cloth that is required is $$624\,m$$.