Curved surface area of a hollow cylinder is $4224\ cm^2$. A rectangular sheet having width $33\ cm$ is formed cutting it along its height. Find perimeter of sheet.

Given: Curved surface area of a hollow cylinder is $4224\ cm^2$. A rectangular sheet having width $33\ cm$ is formed cutting it along its height. 

To do: To find perimeter of sheet.

Solution:

Let $r\ m$ be the radius of base of cylinder and  $h\ m$ be the its height.

Then, Surface Area $=2\pi rh\ cm^2$

$\Rightarrow 2\pi rh=4224$ 

$\Rightarrow  2\pi r ( 33)=4224$                    [$\because h=33\ cm$] 

$\Rightarrow  2\pi r=\frac{4224}{33}$ 

$\Rightarrow  2\pi r=128$ 

Perimeter of base$=128\ cm$ 

Length of sheet $( l)=128\ cm$ 

Breadth of sheet $( b)=33\ cm$ 

Perimeter of rectangular sheet$=2 ( l+b)$

$=2 ( 128+33)$

$=2 ( 161)=322\ cm$

Thus, perimeter of the sheet is $322\ cm$.

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Updated on: 10-Oct-2022

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