Question

the radius of two cylinders are in the ratio 2:3 and their height s are in the ratio 5:3.the ratio of their volume is​

Answer 1

Answer:

Given:

• For the cylinders, ratio of the radius is 2 : 3 and the ratio of heights is 5 : 3.

To find:

• Ratio of their volumes.

Solution:

Let R be the constant for radius and H be the constant for height.

$\boxed{\sf{Volume \ of \ cylinder =\pi\times \ r^{2}\times \ h}} \\ \\ \sf{Ratio \ of \ volumes=\dfrac{\pi\times(2R)^{2}\times5H}{\pi\times(3R)^{2}\times3H}} \\ \\ \sf{\therefore{Ratio \ of \ volumes=\dfrac{4R^{2}\times5H}{9R^{2}\times3H}}} \\ \\ \sf{\therefore{Ratio \ of \ volumes =\dfrac{20}{27}}} \\ \\ \sf{\therefore{Ratio \ of \ volumes=20:27}}$