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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
6 months ago
Dear Student

Lateral surface area of hollow cylinder = 4224 cm^2
Height of hollow cylinder, h = 33 cm and say r be the radius of the hollow cylinder Curved surface area of hollow cylinder = 2πrh
4224 =2×π×r×33
r = (4224)/(2π×33)
r = 64/π
Now, Length of rectangular sheet, l = 2πr
l =2 π×(64/π)= 128 (using value of r)
So the length of the rectangular sheet is 128 cm.
Also, Perimeter of rectangular sheet = 2(l+b) = 2(128+33)
= 322
The perimeter of rectangular sheet is 322 cm.

Thanks

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