A circus tent is cylindrical up to a height of 3 m and conical above it. If its diameter is 105 m and the slant height of the conical part is 63 m, then the total area of the canvas required to make the tent is $$\left( {{\text{take }}\pi = \frac{{22}}{7}} \right)$$

Solution (By Examveda Team)

∴ Radius of cone $$ = \frac{{105}}{2}{\text{m}}$$
Slant height of cone = 63 m
⇒ Curved surface area of cone
$$\eqalign{ & = \pi rl \cr & = \frac{{22}}{7} \times \frac{{105}}{2} \times 63 \cr & = 10395{\text{ }}{{\text{m}}^2} \cr} $$
⇒ Radius of cylinder $$ = \frac{{105}}{2}{\text{m}}$$
Height = 3 m (given)
∴ Curved surface area of cylinder
$$\eqalign{ & = 2\pi rh \cr & = 2 \times \frac{{22}}{7} \times \frac{{105}}{2} \times 3 \cr & = 990{\text{ }}{{\text{m}}^2} \cr} $$
∴ Total curved area of structure
⇒ Curved area of cone + Curved area of cylinder
= 10395 + 990
= 11385 m²
∴ Total area of canvas = 11385 m²