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in Mensuration by (38.0k points)
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Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radius.

2 Answers

+2 votes
by (36.4k points)
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Best answer

Given,

Volume of cylinder 1 = volume of cylinder 2

Ratio of their height = 1 : 2

\(\frac{h_1}{h_2}\) = \(\frac{1}{2}\)

We have,

= V1 = V2

= πr12h1 = πr22h2

\(\frac{r^2_1}{r^2_2}\) = \(\frac{2}{1}\)

\(\frac{r_1}{r_2}\) = \(\sqrt{\frac{2}{1}}\) = \({\frac{\sqrt2}{1}}\)

+2 votes
by (105 points)

Volume of the cylinder is given by:

\(V = \pi r^2h\)

Where r is the radius and h is the height of the cylinder.

We know that:

\(V_1 = V_2 \space\text{and}\space h_1 = 2h_2\)

Therefore:

\(\pi r_1^22h_2 = \pi r_2^2h_2\implies \frac{r_2}{r_1}=\sqrt2\)

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