Question

Sergio has two similar cylindrical pots, Pot $\mathrm{A}$ and Pot $\mathrm{B}$. The radius of Pot $\mathrm{A}$ is $15\mathrm{inches}$ , and the radius of Pot $\mathrm{B}$ is $3\mathrm{inches}$ . What is the ratio of the volume of Pot $\mathrm{A}$ to the volume of Pot $\mathrm{B}$?

• A. $10\mathbf{:}1$
• B. $25\mathbf{:}1$
• C. $125\mathbf{:}1$
• D. $5\mathbf{:}1$

Answer 1

The correct option is B

$25\mathbf{:}1$

Explanation for correct option:

Finding the ratio of the volume of the two cylinder
We know that volume of cylinder $={\mathrm{\pi r}}^2\mathrm{h}$, where $\mathrm{r}$ is radius and $\mathrm{h}$ is height of cylinder.
These two pots are similar then the height will be same for both pots
Ratio of volume of pot $\mathrm{A}$ to the volume of pot $\mathrm{B}$ $=\mathrm{\pi }·{15}^2·\mathrm{h}\mathbf{:}\mathrm{\pi }·3^2·\mathrm{h}$
$$\begin{gathered} =225:9 \\ =25\mathbf{:}1 \end{gathered}$$

Hence, option B is correct.