Question

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

Answer 1

Radius of conical tent, r = 7 m
Height of conical tent, h = 24 m
$$\begin{gathered} \mathrm{Therefore},\mathrm{slant}\mathrm{height},l=\sqrt{r^2+h^2} \\ =\sqrt{7^2+{24}^2} \\ =\sqrt{49+576} \\ =\sqrt{625}=25\mathrm{m} \end{gathered}$$
$$\begin{gathered} \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{conical}\mathrm{tent}=\mathrm{\pi }rl \\ =\frac{22}{7}\times 7\times 25 \\ =22\times 25 \\ =550{\mathrm{m}}^2 \end{gathered}$$

Length of cloth = $\frac{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{tent}}{\mathrm{Width}\mathrm{of}\mathrm{cloth}}=\frac{550{\mathrm{m}}^2}{5\mathrm{m}}=110\mathrm{m}$