question_answer

The ratio of radii of two cylinders 1: 2 and heights are in ratio 2: 3. The ratio of their volumes is?

Answer:

Let

\[{{r}_{1}}\]

and

\[{{r}_{2}}\]

are radii of two cylinders

\[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{1}{2}\]

Let

\[{{h}_{1}}\]

and

\[{{h}_{2}}\]

are heights of two cylinder

\[\frac{{{h}_{1}}}{{{h}_{2}}}=\frac{2}{3}\]

Let

\[{{V}_{1}}\]

and

\[{{V}_{2}}\]

columns of two cylinders

\[\therefore\]

\[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\pi {{r}^{2}}_{1}{{h}_{1}}}{{{\pi }^{2}}_{2}{{h}_{2}}}\]

\[=\frac{1}{4}\times \frac{2}{3}\]

\[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{1}{6}\]