To find the scale factor between the two boxes, we can compare their volumes. We know the volume of the larger box is 648 inches³ and the volume of the smaller box is 24 inches³.
The scale factor can be determined by taking the cube root of the ratio of the volumes, since the scale factor in dimensions (length, width, height) is related to the cube root of the ratio of volumes.
-
Calculate the ratio of the volumes: \[ \text{Volume ratio} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{648}{24} \] \[ \text{Volume ratio} = 27 \]
-
Now, take the cube root of the volume ratio to find the linear scale factor: \[ \text{Scale factor} = \sqrt[3]{27} = 3 \]
Thus, the scale factor between the two boxes is 3.
The answer is: a. 3