Question

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

Answer 1

Let h be the height and r be the radius of the cylinder. Then,

$\frac{2\pi rh}{2\pi rh+2\pi r^2}=\frac{1}{2}$

$\frac{2\pi rh}{2\pi r(h+r)}=\frac{1}{2}$

$\frac{h}{h+r}=\frac{1}{2}$

$2h=h+r$

$h=r$

$h:r=1:1$