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

Given:

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

To do:

We have to find the ratio between the height and radius of the cylinder.

Solution:

We know that,

Curved surface area of a right circular cylinder of height $h$ and radius $r=2\pi rh$.
Total surface area of a right circular cylinder of height $h$ and radius $r=2\pi rh+2\pi r^2=2\pi r(h+r)$.

 Let the height of the right circular cylinder be $h$ and radius be $r$.

Therefore,

$2\pi rh:2\pi r(h+r)=1:2$

$h:(h+r)=1:2$

$2h=1(h+r)$

$2h-h=r$

$h=r$

$h:r=h:h=1:1$

Therefore, the ratio between the height and radius of the cylinder is $1:1$.