Question

Question 6
The radii of two cylinders are in the ratio of 2:3 and their heightsare in the ratio of 5:3. The ratio of their volumes is:

A) 10:17
B) 20:27
C) 17:27
D) 20:37

Answer 1

The answer is B.
Let the radii of two cylinders be $r_1$ and $r_2$ and height of the cylinders be $h_1$ and $h_2$.

Given, $\frac{r_1}{r_2}=\frac{2}{3}and\frac{h_1}{h_2}=\frac{5}{3}$

$\therefore$ Ratio of volumes $=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}={\left(\frac{r_1}{r_2}\right)}^2\left(\frac{h_1}{h_2}\right)$

$={\left(\frac{2}{3}\right)}^2\left(\frac{5}{3}\right)=\frac{4}{9}\times \frac{5}{3}=20:27$

Hence, the ratio of their volumes is 20:27.