Question

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

Answer 1

Let r be the radius and h be the height of a right circular cylinder, then Curved surface area = 2πrh
and total surface area = 2πrh x 2πr² = 2πr(h + r)
But their ratio is 1: 2

`therefore (2pir)/(2pir(h + r)) = 1/2 ⇒ h/(h + r) = 1/2`

⇒ 2h = h + r ⇒ 2h - h = r

⇒ h = r = 1 : 1

Hence their radius and height are equal