Two similar boxes are used for packaging laundry soap. One box has a volume of 648 inches3 ; the other box has a volume of 24 inches^3 . Compare the volumes and determine the scale factor between the two boxes.(1 point)

Responses

2
1/2
3
1

1 answer

To find the scale factor between the two boxes based on their volumes, we can divide the volume of the larger box by the volume of the smaller box.

Volume of the larger box = 648 cubic inches
Volume of the smaller box = 24 cubic inches

Calculating the scale factor:

\[ \text{Scale factor} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{648}{24} = 27 \]

The scale factor of the volumes is 27; however, for similar boxes, the scale factor relating to the linear dimensions (length, width, height) is the cube root of the volume ratio.

Calculating the cube root of the scale factor:

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

Thus, the scale factor between the two boxes in terms of linear dimensions is 3.

The correct response is:

3