To compare the volumes of the two boxes and determine the scale factor, we can start by dividing the volume of the larger box by the volume of the smaller box.
The volume of the larger box is 648 inches³, and the volume of the smaller box is 24 inches³.
Scale factor = Volume of larger box / Volume of smaller box = 648 inches³ / 24 inches³ = 27
This means the scale factor between the two boxes is 27:1. However, this value needs to be expressed in a format given in the options.
Since the problem specifies a similarity and the scale factor is typically expressed in a ratio concerning linear dimensions (instead of volumes), we take the cube root of the scale factor to get the linear scale factor:
\[ \text{Linear scale factor} = \sqrt[3]{27} = 3 \]
Therefore, the scale factor between the two boxes is \(3\).
The correct response is:
3
1 answer