Discussion
Two circular cylinders of equal volume have their heights in the ratio 1: 2. Ratio of their radii is
Answer: B
Equal volumes with heights in the ratio \( 1 : 2 \):
\[ \pi r_{1}^{2} h = \pi r_{2}^{2} (2h) \]
\[ r_{1}^{2} = 2 r_{2}^{2} \quad\Longrightarrow\quad \frac{r_{1}}{r_{2}} = \sqrt{2} \]
So the ratio is \( \sqrt{2} : 1 \). The shorter cylinder must be wider, and because volume depends on \( r^{2} \), halving the height needs only a \( \sqrt{2} \) increase in radius rather than a doubling.
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