Two similar boxes are used for packaging laundry soap. One box has a volume of 648 inches^3; the other box has a volume of 24 inches^3. compare the volumes and determines the scale factor between the two boxes.

Question

A. 1
B. 2
C. 1/2
D. 3

Answer 1

To determine the scale factor between the two boxes, we can compare their volumes. The volume of the larger box is 648 inches³, and the volume of the smaller box is 24 inches³.

The scale factor can be found by taking the cube root of the ratio of the volumes, since the boxes are similar (meaning their dimensions scale proportionately).

1. Calculate the ratio of the volumes: \[ \text{Ratio} = \frac{648}{24} = 27 \]

2. Now find the cube root of the ratio to determine the linear scale factor: \[ \text{Scale Factor} = \sqrt[3]{27} = 3 \]

Thus, the scale factor between the two boxes is \(3\). The correct answer is:

D. 3