Question

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

Answer 1

Ratio of radii of two cylinder = 2:3

Let radius of first cylinder $\left(r_1\right)$ = 2x

and second cylinder $\left(r_2\right)$=3x

and ration in their heights = 5:3

Let height of first cylinder $\left(h_1\right)$=5y

and height of second $\left(h_2\right)$ = 3y

$\therefore$ Volume of the first cylinder

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

and volume of second cylinder

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

Now ration between then,

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

= 20:27