Question

How many metres of cloth 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and whose height is 24 m?

Answer 1

Let l m be the length of the cloth.
Width of the cloth =5 m
Radius of the base of the tent =7 m
Height of the tent =24 m
Now, area of the required cloth = curved surface area of the tent
$$\begin{gathered} l\times 5=\mathrm{\pi }rL \\ \Rightarrow 5l=\frac{22}{7}\times 7\times \sqrt{7^2+{24}^2} \\ \Rightarrow l\mathit{}=\frac{22\times \sqrt{49+576}}{5} \\ =\frac{22\times 25}{5} \\ =110\mathrm{m} \end{gathered}$$

∴ The length of the cloth is 110 m.