MathematicsThe base radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 3:2 the ratio of their volume is

The base radii of two cylinders are in the ratio $2 : 3$ and their heights are in the ratio $3 : 2$ the ratio of their volume is

For two cylinders

: r_{1} : r_{2} = 2 : 3

$h_{1} : h_{2} = 3 : 2$

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

$= {(2)}^{2} \times 3 : {(3)}^{2} \times 2$

$= 12 : 18$

$= 2 : 3$

$∴ V_{1} : V_{2} = 2 : 3$

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