Question:
Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii?
Solution:
Let r1 and r2 be the radii of two right circular cylinders and h1 and h2 be the heights.
Since,
Both the cylinder has the same volume.
Therefore,
$\left(\frac{r_{1}}{r_{2}}\right)^{2}=\frac{h_{2}}{h_{1}}$
$\left(h_{1}: h_{2}=1: 2\right.$, given $)$
$\left(\frac{r_{1}}{r_{2}}\right)^{2}=\left(\frac{2}{1}\right)$
$r_{1}: r_{2}=\sqrt{2}: 1$
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