Let the radii of two cylinders be 2r and 3r respectively and their heights be 5h and 4h respectively. Let S_{1} and S_{2} be curved Surface area of the two cylinders and V_{1} and V_{2} be their volumes.
Then, S_{1} = Curved surface area of the cylinders of height 5h and radius 2r
⇒ 2π × 2r × 5h = 20πrh sq., units
S_{2} = Curved surface area of cylinder of height 4h and radius 3r
= 2π × 3r × 4h = 24πrh
S_{1}/S_{2} = 20πrh/24πrh = 5/6 ⇒ S_{1}: S_{2} = 5 : 6
V_{1} = Volume of cylinder of height 5h and radius 2r = π × (2r)^{2} × 5h = 20πr^{2}h cubic units
V_{2} = Volume of cylinder of height 4h and radius 3r = π × (3r)^{2} × 4h = 36 πr^{2}h cubic units
∴ V_{1}/V_{2} = 20πr^{2}h/36 πr^{2}h = 5/9 ⇒ V_{1} : V_{2} = 5 : 9