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:
Total canvas used = curved area of cylinder + curved area of cone
$=\left(2 \times \frac{22}{7} \times 32.5 \times 3+\frac{22}{7} \times 52.5 \times 53\right) \mathrm{m}^{2}$
$=\frac{22}{7} \times 52.7 \times(6+53) \mathrm{m}^{2}$
$=22 \times 7.5 \times 59$
$=9735 \mathrm{~m}^{2}$
So,
Area of canvas = 9735
Length × width = 9735 m2
Length × 5 = 9735
So length
$=\frac{9735}{5}$
$=1947 \mathrm{mtr}$.