Question

What length of canvas 3 m wide will be required to make a conical tent of height 8 m and radius of base 6 m? (use π = 3.14)

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{conical}\mathrm{tent},h=8\mathrm{m}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{conical}\mathrm{tent},r=6\mathrm{m}\mathrm{and} \\ \mathrm{Widht}\mathrm{of}\mathrm{the}\mathrm{canvas},B=3\mathrm{m} \\ \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{canvas}\mathrm{required}\mathrm{be}L. \\ \mathrm{Also},\mathrm{the}\mathrm{slant}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{conical}\mathrm{tent},l=\sqrt{h^2+r^2} \\ =\sqrt{8^2+6^2} \\ =\sqrt{64+36} \\ =\sqrt{100} \\ =10\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{conical}\mathrm{tent}=\mathrm{\pi }rl \\ =3.14\times 6\times 10 \\ =188.4{\mathrm{cm}}^2 \\ \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{canvas}\mathrm{required}=188.4{\mathrm{cm}}^2 \\ \Rightarrow LB=188.4 \\ \Rightarrow L\times 3=188.4 \\ \Rightarrow L=\frac{188.4}{3} \\ \therefore L=62.8\mathrm{cm} \end{gathered}$$

So, the length of the canvas required to make the conical tent is 62.8 cm.