Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the ratio between the height and radius of the cylinder.

Answer 1

Curved surface area of a cylinder = 2πrh

Total surface area of a cylinder = 2πr(r + h)

The ratio between the curved surface area and the total surface area of a cylinder is 1 : 2.

∴ `1/2 = (2pirh)/(2pir(r + h))`

⇒ `1/2 = h/((r + h))`

⇒ 2h = (r + h)

⇒ 2h – h = r

⇒ h = r

∴ Ratio of height and radius = 1 : 1.