Question

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

• A. $10:1$
• B. $25:1$
• C. $125:1$
• D. $5:1$

Answer 1

The correct option is B

$25:1$

Explanation for correct option:

Step-1: Find the volume of the pot $A$:

The volume of a cylinder is given by ${\mathrm{\pi r}}^2\mathrm{h}$, where $r$ is the radius and $h$ is the height.

The radius of the Pot $A$ is $15$ inches.

Thus, the volume of the cylindrical pot $A$ is

$$\begin{gathered} V_A=\mathrm{\pi }{\left(15\right)}^2\mathrm{h} \\ \therefore =225\mathrm{\pi h} \end{gathered}$$

Step-2: Find the volume of the pot $B$:

The radius of the Pot $B$ is $3$ inches.

Thus, the volume of the cylindrical pot $B$ is

$$\begin{gathered} V_B=\mathrm{\pi }{\left(3\right)}^2\mathrm{h} \\ \therefore =9\mathrm{\pi h} \end{gathered}$$

Step-3: Find the ratio of the volume of the cylindrical pot $A$ to $B$:

The ratio of the volume of the Pot $A$ to Pot $B$ is

$\begin{array}{rcl}\frac{V_A}{V_B}& =& \frac{225\mathrm{\pi h}}{9\mathrm{\pi h}}\\ \therefore & =& \frac{25}{1}\end{array}$

Thus, option (B) is correct.