Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.

Answer 1

We have,

Let radius of cylinder be 'r'.

Let height of cylinder be 'h'.

`("Curved surface area of cylinder")/("total surface area of cylinder") = 1/2`

`(2pirh)/(2pir(h + r)) = 1/2`

`h/((h + r)) = 1/2`

2h = h + r

2h - h = r

h = r

Height = Radius

Hence proved.