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 determine the scale factor between the two boxes. A. 2 B. 1/2 C. 3 D. 1

Answer 1

To determine the scale factor between the two boxes, we need to compare their volumes.

The volume of the larger box is 648 cubic inches, and the volume of the smaller box is 24 cubic inches.

The scale factor can be found by taking the cube root of the ratio of the volumes since the scale factor for similar three-dimensional objects is the cube root of the ratio of their volumes.

First, we calculate the ratio of the two volumes:

\[ \text{Ratio} = \frac{648}{24} = 27 \]

Next, we find the cube root of this ratio to find the linear scale factor:

\[ \text{Scale factor} = \sqrt[3]{27} = 3 \]

Thus, the scale factor between the two boxes is 3.

So, the answer is C. 3.