Question

If the radii of two cylinders are in the ratio 2:3 and their heights are in the ratio of 5:3, then what is the the ratio of their volumes?

• A. 27:17
• B. 20:24
• C. 20:27
• D. 24:30

Answer 1

The correct option is C 20:27

Ratio of the radii of two cylinders = 2:3

Let the radius of first cylinder, $r_1$ = 2x, and that of the second cylinder, $r_2$=3x

Also, given that the ratio of their heights = 5:3

Let the height of first cylinder, $h_1$=5y,and that of the second one, $h_2$ = 3y.

$\therefore$ The volume of the first cylinder

= $\pi r^2$ h =$\pi \times (2x{)}^2\times 5y=20\pi x^{2}y$,

and the volume of second cylinder

=$\pi (3x{)}^2\times 3y=27\pi x^{2}y$

Now, ratio of the volumes of the two cylinders

=$20\pi x^{2}y:27\pi x^{2}y$

= 20:27