Question

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

• A. $4:9$
• B. $9:4$
• C. $20:27$
• D. $27:20$

Answer 1

Answer: (C)

We have,

The, radii of two cylinders are $r_1:r_2=2:3$

Heights are in the ratio. $h_1:h_2=5:3$

Their volume.is $V_1:V_2=?$

We know that,

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

$\frac{V_1}{V_2}=\frac{{r_1}^2{h}_1}{{r_2}^2{h}_2}$

$\frac{V_1}{V_2}={\left(\frac{r_1}{r_2}\right)}^2\frac{h_1}{h_2}$

$\frac{V_1}{V_2}={\left(\frac{2}{3}\right)}^2\frac{5}{3}$

$\frac{V_1}{V_2}=\frac{4}{9}\times \frac{5}{3}$

$\frac{V_1}{V_2}=\frac{20}{27}$

Hence, this is the answer.