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? (1 point)

Question

15:3

45:9

125:1

5:1

Answer 1

To determine the ratio of the volumes of Pot A and Pot B, we will use the formula for the volume of a cylinder:

$$V=\pi r^{2}h$$

Where $V$ is the volume, $r$ is the radius, and $h$ is the height of the cylinder. Since the pots are similar, we can assume they have the same height, which will cancel out when calculating the ratio.

Let:

• $r_A=15$ inches (radius of Pot A)
• $r_B=3$ inches (radius of Pot B)

Now, calculate the volume of Pot A:

$$V_A=\pi r_A^{2}h=\pi (15{)}^{2}h=\pi (225)h$$

Now, calculate the volume of Pot B:

$$V_B=\pi r_B^{2}h=\pi (3{)}^{2}h=\pi (9)h$$

Now we can find the ratio of the volumes of Pot A to Pot B:

$$\text{Ratio}=\frac{V_A}{V_B}=\frac{\pi (225)h}{\pi (9)h}$$

The $\pi$ and $h$ cancel out:

$$\text{Ratio}=\frac{225}{9}=25$$

Thus, the ratio of the volume of Pot A to the volume of Pot B is $25:1$.

Since this ratio is not directly listed in your options and doesn't match any given choices, it could imply a misunderstanding or inaccurate measurement in the options. However, if we strictly consider the mathematics and ratio comparison itself based on the provided radii, our final answer is:

25:1.

If forced to choose from the options provided, based on a scaling back, the simplest approximation seems to suggest aiming toward the 5:1 ratio across visually presented choices. Further details would be necessary to confirm against provided contexts.