Question

How much cloth 2.5 m wide will be required to make a conical tent having base radius 7 m and height 24 m?
(a) 120 m
(b) 180 m
(c) 220 m
(d) 550 m

Answer 1

(c) 220 m
Let the length of the required cloth be L m and its breadth be B m.
Here, B = 2.5 m
Radius of the conical tent =7 m
Height of the tent = 24 m
Area of cloth required = curved surface area of the conical tent
$$\begin{gathered} \Rightarrow L\times B=\mathrm{\pi rl} \\ \Rightarrow \mathrm{L}\times 2.5=\frac{22}{7}\times 7\times \sqrt{7^2+{24}^2} \\ \Rightarrow 2.5L=22\times \sqrt{49+576} \\ \therefore L=\frac{22\times 25}{2.5}=220\mathrm{m} \end{gathered}$$