Question

The ratio of the base radii of two right circular cylinders having the same height is 4 : 5. The ratio of their volumes will be :

• A. 4 : 25
• B. 16 : 25
• C. 4 : 5
• D. 16 : 5

Answer 1

The correct option is B

16 : 25

Let $r_1$ and $h_1$ be the radius and height of the first cylinder and $r_2$ and $h_2$ be the radius and height of the second cylinder.

Ratio of their volumes $=\frac{V_1}{V_2}$

$\frac{V_1}{V_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}=\frac{r_1^{2}h}{r_2^{2}h}\text{Since}{h}_1=h_2$

$\frac{V_1}{V_2}={\left(\frac{r_1}{r_2}\right)}^2={\left(\frac{4}{5}\right)}^2=\frac{16}{25}$

Hence the ratio of their volumes = 16:25