The radii of the bases of two cylinder are in the ratio of $3 : 4$ respectively and their heights are in the ratio $2 : 3$ respectively. Find the ratio of their volumes.

6 : 7

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3 : 8

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11 : 7

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8 : 9

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Solution

The correct option is B $3 : 8$
Given ratio of bases of two cylinders is $3 : 4$ and heights in ratio $2 : 3$ .
We k.n.t Volume of cylinder ( $V) = π r^{2} h$ .
$r_{1} : r_{2} = 3 : 4$ and $h_{1} : h_{2} = 2 : 3$ .

$\Rightarrow V_{1} : V_{2} = (π r_{1}^{2} h_{1}) : (π r_{2}^{2} h_{2}) = r_{1}^{2} h_{1} : r_{2}^{2} h_{2}$

$r_{1}^{2} : r_{2}^{2} = 3^{2} : 4^{2} = 9 : 16$ ( $∵ r_{1} : r_{2} = 3 : 4$ )

$\Rightarrow V_{1} : V_{2} = 9 \times 2 : 16 \times 3 = 3 : 8$

Ratio of volumes is $3 : 8$ .

Option (B) is correct.

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The radii of the bases of two cylinder are in the ratio of 3:4 respectively and their heights are in the ratio 2:3 respectively. Find the ratio of their volumes.

The radii of the bases of two cylinder are in the ratio of $3 : 4$ respectively and their heights are in the ratio $2 : 3$ respectively. Find the ratio of their volumes.