The radius of two cylinders are in the ratio $2 : 3$ and their heights are in the ratio $3 : 5$ . Find the ratio of their volumes.
$\frac{2}{3}$
$\frac{4}{15}$
$\frac{3}{2}$
$\frac{3}{5}$

Question

The radius of two cylinders are in the ratio 2-3 and their heights are in the ratio 3-5- Find the ratio of their volumes-dfrac-2-3-dfrac-4-15-dfrac-3-2-dfrac-3-5-

Toppr Admin · Accepted Answer

For Cylinder 1-r1-2xh1-3yFor Cylinder 2-r2-3xh2-5yRatio of the volumes-x3C0-r21h1-x3C0-r22h2-x3C0-xD7-4x2-xD7-3y-x3C0-xD7-9x2-xD7-5y-x21D2-415

The radius of two cylinders are in the ratio 2:3 and their heights are in the ratio 3:5. Find the ratio of their volumes.234153235

For Cylinder 1:r1=2xh1=3yFor Cylinder 2:r2=3xh2=5yRatio of the volumes=πr21h1πr22h2=π×4x2×3yπ×9x2×5y⇒415

The radius of two cylinders are in the ratio $2 : 3$ and their heights are in the ratio $3 : 5$ . Find the ratio of their volumes.
$\frac{2}{3}$
$\frac{4}{15}$
$\frac{3}{2}$
$\frac{3}{5}$

For Cylinder $1$ :
$r_{1} = 2 x$
$h_{1} = 3 y$
For Cylinder $2$ :
$r_{2} = 3 x$
$h_{2} = 5 y$
Ratio of the volumes $= \frac{π r_{1}^{2} h_{1}}{π r_{2}^{2} h_{2}}$
$= \frac{π \times 4 x^{2} \times 3 y}{π \times 9 x^{2} \times 5 y}$
$\Rightarrow \frac{4}{15}$