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The lateral surface area of a hollow cylinder is 4224 $cm 2$ . It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet.

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322 cm

332 cm

341 cm

350 cm

answer is A.

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Detailed Solution

It is given that the lateral surface area of the cylinder is

and height of cylinder h is 33 cm.
Let radius of the cylinder = r cm.
Lateral surface area of cylinder is

2 π r h

⇒ L . S . A = 2 π r h ⇒ 4224 = 2 × π × r × 33 ⇒ r = 4224 2 π × 33 ⇒ r = 64 π … … (1)

The circumference of the base of cylinder is equal to the length of the sheet
Next length of rectangular sheet,

l = 2 π r

Substituting value of r from equation 1,

⇒ l = 2 π × 64 π ⇒ l = 128 c m

So, the length of the rectangular sheet is 128 cm.
Therefore, the perimeter of rectangular sheet,

⇒ 2 (l + b) ⇒ 2 (128 + 33) ⇒ 322 c m

The perimeter of the rectangular sheet is 322 cm.
Hence option (1) is correct.

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