The ratio between the radius of the base and height of a cylinder is 2 : 3. If its volume is 1617 cm³, find the total surface area of the cylinder.

Given,

Volume of cylinder = 1617 cm³

Let radius of cylinder = 2x cm

Let height of cylinder = 3x cm

= πr²h = 1617

=

= x³ =

= x = 3.5 cm

So radius = 2x = 2 ×3.5 = 7 cm

Height = 3x = 3×3.5 = 10.5 cm

∴ total surface area of cylinder = 2πr(h+r)

= ²