Question

The radii of two cylinders are in the ratio 3:5. Their heights are in the ratio 10:6. Find the ratio of their volumes.

• A. $\frac{9}{25}$
• B. $\frac{3}{5}$
• C. $\frac{9}{16}$
• D. $\frac{3}{16}$

Answer 1

The correct option is B

$\frac{3}{5}$

Let the radius of the Ist cylinder be $r_1$ and height be $h_1$

Let the radius of the IInd cylinder be $r_2$ and height be $h_2$

$\frac{\text{Volume of Ist cylinder}}{\text{Volume of IInd cylinder}}=\frac{\pi r_1^{2}h1}{\pi r_2^{2}h2}$

$={\left(\frac{r1}{r2}\right)}^2\times \frac{h1}{h2}$

$={\left(\frac{3}{5}\right)}^2\times \frac{10}{6}$

$=\frac{3}{5}$

Hence the raio of their volumes is 3:5