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 = $2\mathrm{\pi }r{h}_1=2\mathrm{\pi }\times 28\times 6=336\mathrm{\pi }$
Curved surface area of the cylinder, CSA₂ will be
$$\begin{gathered} \mathrm{\pi }rl=\mathrm{\pi }r\left(\sqrt{h^2+r^2}\right)=\mathrm{\pi }\times 28\times \left(\sqrt{{21}^2+{28}^2}\right)=28\mathrm{\pi }\left(\sqrt{441+784}\right) \\ =28\mathrm{\pi }\times 35 \\ =980\mathrm{\pi } \end{gathered}$$
Total curved surface area = CSA of cylinder + CSA of cone
= CSA₁ + CSA₂
$$\begin{gathered} =336\mathrm{\pi }+980\mathrm{\pi } \\ =1316\mathrm{\pi } \\ =4136{\mathrm{m}}^2 \end{gathered}$$
Thus, the area of the canvas used in making the tent is 4136 m² .