Question

If curved surface area of solid cylinder is two third of its total surface area, then
find the ratio of its height and radius.

Answer 1

Given :

Curved surface area of solid cylinder is two third of its total surface area.

To Find :

The ratio of its height and radius.

Solution :

Let, height and radius of cylinder is h and r.

Curved surface area is given by :

$CSA =2\pi r h$

Total surface area is given by :

$TSA = 2\pi r h + 2\pi r ^2\\\\TSA = 2\pi r( h + r )$

It is given that, CSA = 2/3 ( TSA )

$2\pi rh = \dfrac{2}{3} \times 2\pi r( h + r)\\\\h = \dfrac{2}{3}( h + r )\\\\3h = 2h + 2r \\\\\dfrac{h}{r} = 2$

Therefore, the ratio of height and radius is 2 : 1 .