Question

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 24 metres?

Answer 1

Radius of the conical tent, r = 7 m
Height of the conical tent, h = 24 m
$$\begin{gathered} \mathrm{Now},l=\sqrt{r^2+h^2} \\ =\sqrt{49+576} \\ =\sqrt{625} \\ =25\mathrm{m} \end{gathered}$$

$$\begin{gathered} \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cone}=\mathrm{\pi }rl \\ =\frac{22}{7}\times 7\times 25 \\ =550{\mathrm{m}}^2 \\ \mathrm{Here},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cloth}=\mathrm{curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cone}=550{\mathrm{m}}^2 \end{gathered}$$

Width of the cloth = 2.5 m
∴ Length of the cloth = $\frac{\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cloth}}{\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{cloth}}=\frac{550}{2.5}=220\mathrm{m}$