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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?
Solution
Curved surface area of cylinder = 4224 cm2
Height of cylinder = 33 cm
Curved surface area of cylinder = 2πrh
`2 × 22/7 × r × 33 = 4224`
r = `(4224 × 7)/(2 × 22 × 33)`
r = `224/11` cm
converting it into a rectangular sheet
Its width = 33 cm
Length of rectangular sheet = circumference of circle
l = 2πr
l = `2 × 22/7 × 224/11` = 128 cm
Then perimeter of rectangular sheet = 2(l + b)
= 2(128 + 33)
= 2 × 161
= 322 cm
Hence, perimeter of rectangular sheet = 322 cm
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