We have,
Dimensions of rectangular sheet = 30 cm × 18 cm
Case (i)
When paper is rolled along its length
2 πr = 30
r = 30 / 2π cm
Height = 18 cm
Volume of cylinder, V1 = πr2h
= π × (30/2π)2 × 18 cm3
Case (ii)
When paper is rolled along its breadth
2πr = 18
r = 18/2π cm
Height = 30 cm
Volume of cylinder, V2 = πr2h
= π × (18/2π)2 × 30 cm3
Hence,
Volume of cylinder,V1 / Volume of cylinder,V2 = {π × (30/2π)2 × 18}/{π × (18/2π)2× 30}
= {π × (30/2π)2 × 18}×1/{π × (2π/18)2× 30}
= 302 × 18 / 182 × 30
= 30/18
= 5/3
∴ The ratio of two volumes is 5:3