To find the scale factor between the two similar boxes, we can compare their volumes. The volume of the larger box is 648 cubic inches, and the volume of the smaller box is 24 cubic inches.
To determine the scale factor based on the volumes, we can use the formula for the scale factor of similar three-dimensional shapes, which is the cube root of the ratio of their volumes.
- Calculate the ratio of the volumes:
\[ \text{Ratio} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{648}{24} = 27 \]
- Find the scale factor by taking the cube root of the ratio:
\[ \text{Scale factor} = \sqrt[3]{27} = 3 \]
Thus, the scale factor between the two boxes is 3.
Therefore, the correct answer is: D. 3
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