The diameters of two cylinders are in the ratio 2:3 Find the ratio of their heights if their volume is the same

3:2

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6:5

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9:4

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9:5

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Solution

The correct option is C 9:4
$d_{1} : d_{2} = 2 : 3$
$h_{1} : h_{2} = ?$
$r_{1} : r_{2} = 1 : 1.5$
$V_{1} = V_{2}$
$∴ π r_{1}^{2} h_{1} = π r_{2}^{2} h_{2}$
$∴ 1^{2} h_{1} = {1.5}^{2} h_{2}$
$∴ \frac{h_{1}}{h_{2}} = \frac{2.25}{1} = \frac{225}{100} = \frac{9}{4}$ '

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