A circus tent is cylindrical to a height of 3 meters 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 2.5 m wide to make the required tent.

From figure,

Radius of conical part = radius of cylindrical part = r.

Radius of the cylindrical part of the tent (r) = $\dfrac{\text{diameter}}{2} = \dfrac{105}{2} \text{ m}$

Radius of the conical part (r) = $\dfrac{105}{2} \text{ m}$

Slant height (l) = 53 m

So, the total curved surface area of the tent = 2πrh + πrl

$= 2 \times \dfrac{22}{7} \times \dfrac{105}{2} \times 3 + \dfrac{22}{7} \times \dfrac{105}{2} \times 53 \\[1em] = \dfrac{13860}{14} + \dfrac{122430}{14} \\[1em] = 990 + 8745 \\[1em] = 9735 \text{ m}^2.$

Width of the canvas used = 2.5 m

Length of canvas = $\dfrac{\text{area of canvas}}{\text{width of canvas}} = \dfrac{9735}{2.5}$ = 3894 m.

Hence, length of the canvas required to make tent is 3894 m.