Question

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

Step-by-step explanation:

Given:Curved Surface area= 4224 cm².

Width of the rectangular sheet = 33 cm

Find: the perimeter of rectangular sheet?

Step by step explanation: Curved Surface area of hollow cylinder= Area of rectangular sheet

4224=length ×breadth

4224=l×33

l= 4224/33

l =128

Perimeter of rectangular sheet = 2×(length+breadth)

Perimeter of rectangular sheet = 2×(128+33)

Perimeter of rectangular sheet = 2×161

Perimeter of rectangular sheet = 322 cm.

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Answer 2

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.

Solution :-

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

Let,

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

As we know that :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}\: \: \: \bigstar$

According to the question by using the formula we get,

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

$\implies \sf 4224 =\: Length \times Breadth$

$\implies \sf 4224 =\: l \times 33$

$\implies \sf \dfrac{4224}{33} =\: l$

$\implies \sf 128 =\: l$

$\implies \sf\bold{\purple{l =\: 128\: cm}}$

Hence, the length of a rectangular sheet is 128 cm.

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

As we know that :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}\: \: \: \bigstar$

Given :

• Length = 128 cm
• Breadth = 33 cm

According to the question by using the formula we get,

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

$\implies \sf Perimeter_{(Rectangular\: Sheet)} =\: 2(161)$

$\implies \sf Perimeter_{(Rectangular\: Sheet)} =\: 2 \times 161$

$\implies \sf\bold{\red{Perimeter_{(Rectangular\: Sheet)} =\: 322\: cm^2}}$

$\therefore$ The perimeter of a rectangular sheet is 322 cm² .