Question

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

Answer 1

Note: Curved surface area of cylinder $=2\pi rh$

Total surface area $=2\pi rh+2\pi r^2$

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

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

$\Rightarrow 2h=h+r$

$\Rightarrow h=r$

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

$\therefore$ required ratio $h:r=1:1$