To determine the scale factor between the two boxes based on their volumes, you can divide the volume of the larger box by the volume of the smaller box.
The volumes are:
- Larger box: 648 inches³
- Smaller box: 24 inches³
Now, calculate the scale factor:
\[ \text{Scale Factor} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{648}{24} \]
Calculating the division:
\[ \frac{648}{24} = 27 \]
However, the scale factor for similar geometric shapes is often expressed in terms of length ratios. Since the scale factor in volume is the cube of the linear scale factor, we need to find the cube root of the volume scale factor.
To find the linear scale factor (let's call it \(k\)), we take the cube root of the volume scale factor:
\[ k = \sqrt[3]{27} = 3 \]
Thus, the scale factor between the two boxes (in terms of length) is 3.
So the answer is 3.
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