To find the scale factor between the volumes of the two boxes, we can divide the volume of the larger box by the volume of the smaller box.
Given:
- Volume of the larger box = 648 inches³
- Volume of the smaller box = 24 inches³
Scale factor = Volume of larger box / Volume of smaller box
Calculating:
\[ \text{Scale Factor} = \frac{648}{24} = 27 \]
However, it seems that neither 2, 3, 1, nor 12 are available as options. Therefore, we must look for any potential relationship in scale factors based on side lengths, assuming the boxes are similar.
Because the boxes are similar, the relationship between the volumes is proportional to the cube of the scale factor \( k \): \[ k^3 = \frac{648}{24} = 27 \]
To find the scale factor \( k \), we take the cube root of 27: \[ k = \sqrt[3]{27} = 3 \]
Therefore, the scale factor between the two boxes is 3.