Given,
Dimensions of rectangular sheet = 30 cm × 0.18 cm
Case (i)
When sheet is rolled along its length:
= 2πr = 30
= r = \(\frac{30}{2π}\)
height of cylinder = 18 cm
Hence, Volume of cylinder thus formed = V1 = \(\frac{22}{7}\) x \((\frac{30}{2π})^2\) x 18 cm3
Case (ii)
When sheet is rolled along its breadth:
= 2πr = 18
= r = \(\frac{18}{2π}\)
Height of cylinder = 30 cm
Volume of cylinder = V2 = \(\frac{22}{7}\) x \((\frac{18}{2π})^2\) x 30 cm3
Hence,
\(\frac{V_1}{V_2}\) = \(\frac{[\frac{22}{7}\times 900\times 4π^2\times 18]}{[\frac{22}{7}\times 324\times 4π^2\times 30]}\) = \(\frac{30}{18}\) = \(\frac{5}{3}\)