Question

The radii of two cylinders are in the ratio of $3:4,$ and their height are in the ratio $4:3.$ The ratio of their volume is :

• A. $4:5$
• B. $4:3$
• C. $3:4$
• D. $5:4$

Answer 1

The correct option is C $3:4$

Let radius of first cylinder $=r_1$

and height of the first cylinder $=h_1$

$\therefore$ Volume of first cylinder, $V_1=\pi r_1^2{h}_1$

Let radius of second cylinder $=r_2$

& height of second cylinder $=h_2$

$\therefore$ Volume of second cylinder, $V_2=\pi r_2^2{h}_2$

Also, $\frac{r_1}{r_2}=\frac{3}{4}\&\frac{h_1}{h_2}=\frac{4}{3}$

Now, $\frac{V_1}{V_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}={\left(\frac{r_1}{r_2}\right)}^2\times \frac{h_1}{h_2}={\left(\frac{3}{4}\right)}^2\times \frac{4}{3}$

$\frac{V_1}{V_2}=\frac{9}{16}\times \frac{4}{3}=\frac{3}{4}$

$\therefore V_1:V_2=3:4$