Question 41

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

Solution

V1 and V2 be the volumes of the cylinder

given that V1 = V2

$$ V1 = \pi r1^2 h1 $$

$$ V2 = \pi r2^2 h2 $$

$$ \pi r1^2 h1 = \pi r2^2 h2 $$

$$ r1^2 h1 = r2^2 h2 $$

given that $$ \frac{h1}{h2} =\frac{2}{1} $$

$$ \frac{r1^2}{r2^2} = \frac{h1}{h2} =\frac{2}{1} $$

solving $$ \frac{r1}{r2} = \frac{\sqrt{2}}{1} $$

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