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.
1 answer