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?

Answer 1

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