Question

$\bf \longrightarrow \: Simple \:Question...$
The lateral surface area of a hollow cylinder is 4224 cm².
It is cut along its height and formed a rectangular sheet
of width 33 cm. Find the perimeter of rectangular sheet?

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Answer 1

❍ Given :-

• Hollow cylinder is converted into rectangular sheet
• Lateral/Curved Surface Area of hollow cylinder is 4224 cm²
• Width of rectangular sheet is 33 cm

❍ To Find :-

• The perimeter of rectangular sheet

❍ Solution :-

Since, hollow cylinder is converted into rectangular sheet therfore, area must be same.

∴ Lateral Surface of hollow cylinder = Area of Rectangular Sheet

→ 4224 = Length × Breadth

→ 4224 = Length × 33

→ $\dfrac{4224}{33} = l$

→ $l = \dfrac{\cancel{4224}}{\cancel{33}}$

→ $\fbox \green{Length = 128 cm}$

➸ Now,

Perimeter of sheet = 2(Length + Breadth)

= 2(128 + 33)

= 2 × 161

= $\fbox \red{322 cm}$

Hence, Perimeter the rectangular sheet is 322 cm.

Answer 2

Answer:

Given :-

• The lateral surface area of a hollow cylinder is 4224 cm².
• It is cut along its height and formed a rectangular sheet of width 33 cm.

To Find :-

• What is the perimeter of a rectangular sheet.

Formula Used :-

$\clubsuit$ Area Of Rectangle Formula :

$\small \longrightarrow \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Width}}}$

$\clubsuit$ Perimeter Of Rectangle Formula :

$\small \longrightarrow \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Width)}}}$

Solution :-

First, we have to find the length of a rectangular sheet :-

Let,

$\mapsto \bf Length_{(Rectangular\: Sheet)} =\: x\: cm$

Given :

• L.S.A or C.S.A of Hollow Cylinder = 4224 cm³
• Width of Cylinder = 33 cm

According to the question by using the formula we get,

$\footnotesize \leadsto \bf Area_{(Rectangular\: Sheet)} =\: L.S.A_{(Hollow\: Cylinder)}$

$\leadsto \sf Length \times Width =\: 4224$

$\leadsto \sf x \times 33 =\: 4224$

$\leadsto \sf 33x =\: 4224$

$\leadsto \sf x =\: \dfrac{\cancel{4224}}{\cancel{33}}$

$\leadsto \sf\bold{\purple{x =\: 128\: cm}}$

Hence, the required length of a rectangular sheet is :

$\implies \sf Length_{(Rectangular\: Sheet)} =\: x\: cm$

$\implies \sf\bold{\green{Length_{(Rectangular\: Sheet)} =\: 128\: cm}}$

Now, we have to find the perimeter of a rectangular sheet :-

Given :

• Length of Cylinder = 128 cm
• Width of Cylinder = 33 cm

According to the question by using the formula we get,

$\small \dashrightarrow \bf Perimeter_{(Rectangular\: Sheet)} =\: 2(Length + Width)$

$\dashrightarrow \sf Perimeter_{(Rectangular\: Sheet)} =\: 2(128 + 33)$

$\dashrightarrow \sf Perimeter _{(Rectangular\: Sheet)} =\: 256 + 66$

$\dashrightarrow \sf\bold{\red{Perimeter_{(Rectangular\: Sheet)} =\: 322\: cm}}$

$\therefore$ The perimeter of rectangular sheet is 322 cm .

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