Multiple choice

The lateral surface area of a hollow cylinder is $5632 cm^{2}$. It is cut along its height and rectangular sheet of width $44 cm$ is formed. Find the perimeter of the rectangular sheet?

  1. $344 cm$
  2. $388 cm$
  3. $320 cm$
  4. $300 cm$
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A Correct answer
Explanation

Lateral surface area = 2 * pi * r * h = 5632. When cut, it forms a rectangle with width 44. If width is height, h = 44. 2 * pi * r * 44 = 5632. 2 * pi * r = 128 (circumference). Perimeter of rectangle = 2 * (length + width) = 2 * (128 + 44) = 2 * 172 = 344.

AI explanation

When the hollow cylinder is cut along its height, its lateral surface area of 5632 sq cm becomes the area of the rectangular sheet. With a width of 44 cm, the length of the sheet is 5632 divided by 44, which equals 128 cm. Using the rectangle perimeter formula, the perimeter is 2 times the sum of 128 and 44, giving 344 cm.

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