A circus tent is in the shape of a 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.

Given:

A circus tent is in the shape of a cylinder surmounted by a conical top of same diameter.

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.

To do:

We have to find the area of the canvas used in making the tent.

Solution:

Diameter of the base of the cylinder $= 56\ m$

Radius of the base of the cylinder $r=\frac{52}{2}$

$= 28\ m$

Height of the tent $= 27\ m$

Height of the cylinder $= 6\ m$

Height of the conical portion $= 27 - 6$

$= 21\ m$

Radius of the conical portion $r = 28\ m$

Slant height of the cone $l=\sqrt{r^{2}+h^{2}}$

$=\sqrt{28^{2}+21^{2}}$

$=35 \mathrm{~m}$

Area of the canvas used $=$ Curved surface area of the cylinder $+$ Curved surface area of the cone

$=2 \pi r h+\pi r l$

$=\frac{22}{7} \times 28(12+35)$

$=4136 \mathrm{~m}^{2}$

The area of the canvas used in making the tent is $4136\ m^2$.

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Updated on: 10-Oct-2022

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