Question

# Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radii.

Solution

## Here, V1 = Volume of cylinder 1          V2 = Volume of cylinder 2           r1 = Radius of cylinder 1           r2 = Radius of cylinder 2           h1 = Height of cylinder 1           h2 = Height of cylinder 2 Volumes of cylinder 1 and 2 are equal. Height of cylinder 1 is half the height of cylinder 2. ​∴ V1 = V2 (πr12h1) = (πr22h2)  (πr12h) = (πr222h)  $\frac{{{r}_{1}}^{2}}{{{r}_{2}}^{2}}=\frac{2}{1}$ $\frac{{r}_{1}}{{r}_{2}}=\sqrt{\frac{2}{1}}$ Thus, the ratio of their radii is $\sqrt{2}$ : 1.MathematicsRD Sharma (2019, 2020)All

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