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

${\displaystyle 2\times \frac{22}{7}\times r\times 33=4224}$

r = ${\displaystyle \frac{4224\times 7}{2\times 22\times 33}}$

r = ${\displaystyle \frac{224}{11}}$ cm

converting it into a rectangular sheet

Its width = 33 cm

Length of rectangular sheet = circumference of circle

l = 2πr

l = ${\displaystyle 2\times \frac{22}{7}\times \frac{224}{11}}$ = 128 cm

Then perimeter of rectangular sheet = 2(l + b)

= 2(128 + 33)

= 2 × 161

= 322 cm

Hence, perimeter of rectangular sheet = 322 cm