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

r12h1) = (πr22h2

r12h) = (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 $\sqrt{2}: 1$.