Question

A circus tent is in the shape of cylinder surmounted by a conical top of same diameter. If their common diameter is 56 m, the height of the cylindrical part is 6 m and the total height of the tent above the ground is 27 m, find the area of the canvas used in making the tent.

Answer 1

Total height of the tent above the ground = 27 m
Height of the cylinderical part,

\[h_1\]= 6 m
Height of the conical part,

\[h_2\] = 21 m
Diameter = 56 m
Radius = 28 m
Curved surface area of the cylinder, CSA₁ = \[2\pi r h_1 = 2\pi \times 28 \times 6 = 336\pi\]

Curved surface area of the cylinder, CSA₂ will be

\[\pi rl = \pi r\left( \sqrt{h^2 + r^2} \right) = \pi \times 28 \times \left( \sqrt{{21}^2 + {28}^2} \right) = 28\pi\left( \sqrt{441 + 784} \right)\]

\[ = 28\pi \times 35\]

\[ = 980\pi\]

Total curved surface area = CSA of cylinder + CSA of cone
= CSA₁ + CSA₂

\[= 336\pi + 980\pi\]

\[ = 1316\pi\]

\[ = 4136 m^2\]

Thus, the area of the canvas used in making the tent is 4136 m².