Question

The lateral surface area of hollow cylinder is 4224 sq cm. It is cut along its height and formed a rectangular sheet of width 48 cm. Find the perimeter of the rectengular sheet.​

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{\boxed { \huge \mathcal\red{ solution}}}}$

Now according to the Question the hollow cylinder is cut along its height and a rectangular sheet is formed.

• So the area of the rectangular sheet will be equal to the L.S.A. of the cylinder,
• and the width of the sheet will be the height of the cylinder,

Now

for a cylinder of base radius r and height h

lateral surface area or L.S.A. is given by the formula stated below:-

$\: \: \: \: \: \large \rightarrow \: \: \boxed{ { \red{\boxed{ \boxed{ L.S.A = 2\pi rh}}}}} \: \: \leftarrow$

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• Given

$\rightarrow L.S.A.=4224 \:cm{}^{2}\\and\\</p><p>\rightarrow h=48 \:cm{}^{2}$

$\implies2\pi rh = 4224 \\ \implies \: 2 \times \frac{22}{7} \times r \times 48 = 4224 \\ \implies r = 4224 \times \frac{7}{2 \times 22 \times 48} \\ \implies \boxed{r = 14 \: cm}$

And the length of the rectangular sheet will be the circumference of the base circle

i.e., length of the sheet

=2πr=2(22/7)(14)cm=88cm

therefore, perimeter of the sheet

$\implies \: perimeter = 2(length + width) \\ \implies perimeter = 2(88 + 48)cm \\ \implies \boxed{ perimeter = 272 \: cm}$

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Another way

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• the area of the rectangular sheet will be equal to the L.S.A. of the cylinder,

So,area of the rectangular sheet=4224 cm²

now for a rectangular sheet area is

$\implies \boxed{Area=length \times width}$

$\implies 4224=length \times 48\\ \implies length=\frac{4224}{48}\\ \implies length=88\: cm$

therefore, perimeter of the sheet

$\implies \: perimeter = 2(length + width) \\ \implies perimeter = 2(88 + 48)cm \\ \implies \boxed{ perimeter = 272 \: cm}$

Hope this helps you......

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