Question

The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3.$The ratio of their volumes will be

(a) $4:9$

(b) $9:4$

(c) $20:27$

(d) $27:20$

Answer 1

The correct option is (c) $20:27$

Given: Ratio of radii of two cylinder $=2:3$

and, the ratio of their heights $=5:3$

Let $r_1=$ radius of $1$st cylinder $=2x$

$r_2=$ radius of $2$nd cylinder $=3x$

$h_1=$ height of $1$st cylinder $=5y$

$h_1=$ height of $2$st cylinder $=3y$

$\therefore \frac{\text{Volume~of~first~cylinder}}{\text{Volume~of~second~cylinder}}$

$=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$

$=\frac{(2x{)}^2\times 5y}{(3x{)}^2\times 3y}$

$=\frac{4x^2\times 5y}{9x^2\times 3y}$

$=\frac{20x^{2}y}{27x^{2}y}$

$=\frac{20}{27}$

$\therefore$ Ratio of volumes $=20:27$