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

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

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

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

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

Hence , the required ratio is $1:1$ .

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