Question

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

Answer 1

Let the radii of cylinders be 2a and 3a
And the height of cylinders be 5b and 3b

Now,
$\frac{volume \: of \: first \: cylinder}{volume \: of \: second \: cylinder}=\frac{\pi \times {4a}^{2} \times 5b}{\pi \times 9 {a}^{2} \times 3b } \\ = \frac{20}{27}$

Answer 2

let R and r be the radius of cylinder 1 and 2
H and h be the height of cylinder 1 and 2
R:r=2:3
R=2,r=3
H:h=5:3
H=5,h=3
ratio of the their volume =volume of cylinder 1/volume of cylinder 2
=PiR^2h:pir^2H
=R^2H/r^2h
=(2x2x5)/(3x3x3)
=2O/27
=0.740