Question

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, then find the total area of the canvas required.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{part},H=4\mathrm{m}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{base},r=\frac{105}{2}\mathrm{m}\mathrm{and} \\ \mathrm{Slant}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{conical}\mathrm{part},l=40\mathrm{m} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{total}\mathrm{area}\mathrm{of}\mathrm{canvas}\mathrm{required}=\mathrm{CSA}\mathrm{of}\mathrm{conical}\mathrm{part}+\mathrm{CSA}\mathrm{of}\mathrm{cylindrical}\mathrm{part} \\ =\mathrm{\pi }rl+2\mathrm{\pi }rH \\ =\mathrm{\pi }r\left(l+2H\right) \\ =\frac{22}{7}\times \frac{105}{2}\times \left(40+2\times 4\right) \\ =11\times 15\times 48 \\ =7920{\mathrm{m}}^2 \end{gathered}$$

So, the area of the canvas required to make the tent is 7920 m².