A circus tent is cylindrical to a height of 3 metres and conical above it.
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.

Solution:

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, = 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

$=\pi r l+2 \pi r H$

$=\frac{22}{7} \times \frac{105}{2}(53+2 \times 3)$

$=\frac{22}{7} \times \frac{105}{2} \times(53+6)$

$=9735 \mathrm{~m}^{2}$

But area of the canvas = length ×× breadth

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