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

$Let\;height\;and\;radius\;of\;the\;cylinder\;be\;h\; and\;r \;respectively\\* curved\;surface\;area=2 \Pi r h\\* total\;surface\;area=2\Pi rh +2\Pi r^2=2\Pi r(h+r)\\* Given\;that\;the\;ratio\;between\;curved\;surface\;and\;total\;surface\;area\;is\;1:2\\*So, \\*\indent \Rightarrow \frac{2\Pi rh}{2\Pi r(h+r)}=\frac{1}{2}\\* \indent \Rightarrow \frac{h}{r+h}=\frac{1}{2}\\*\indent \Rightarrow 2h=r+h\\* \indent \Rightarrow r=h \\*So, \\* \indent \frac{h}{r}=\frac{1}{1}\\* Hence,\; the\; ratio\; between\; height\; and\; radius\; of\; the\;cylinder\; is\; 1:1$

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