Question

A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.

Answer 1

Radius of the tent, r = 52.5 m
Height of the cylindrical portion of the tent, H = 3 m
Slant height of the conical portion of the tent, l = 53 m
The tent is a combination of a cylindrical and a conical portion.
i.e., area of the canvas = curved surface area of the cone + curved surface area of the cylinder
= $\mathrm{\pi }rl+2\mathrm{\pi }rH$
$$\begin{gathered} =\frac{22}{7}\times \frac{105}{2}\left(53+2\times 3\right) \\ =\frac{22}{7}\times \frac{105}{2}\times \left(53+6\right) \\ =9735{\mathrm{m}}^2 \end{gathered}$$

But area of the canvas = length $\times$ breadth

∴ Length of the canvas = $\frac{\mathrm{area}}{\mathrm{breadth}}=\frac{9735}{5}=1947\mathrm{m}$