Question
Two similar boxes are used for packaging laundry soap. One box has a volume of 648 inches3
648
inches
3
; the other box has a volume of 24 inches3
24
inches
3
. Compare the volumes and determine the scale factor between the two boxes.(1 point)
Responses
1
1
3
3
2
2
12
648
inches
3
; the other box has a volume of 24 inches3
24
inches
3
. Compare the volumes and determine the scale factor between the two boxes.(1 point)
Responses
1
1
3
3
2
2
12
Answers
GPT-4o mini
To find the scale factor between the two boxes, we 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 calculated by dividing the volume of the larger box by the volume of the smaller box:
\[
\text{Scale Factor} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{648}{24} = 27
\]
The scale factor between the two boxes is 27 in terms of volume. However, since the boxes are similar, the scale factor for their linear dimensions (length, width, height) would be the cube root of the volume scale factor:
\[
\text{Linear scale factor} = \sqrt[3]{27} = 3
\]
So, the correct response to the scale factor (in linear dimensions) between the two boxes is:
**3**
The scale factor can be calculated by dividing the volume of the larger box by the volume of the smaller box:
\[
\text{Scale Factor} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{648}{24} = 27
\]
The scale factor between the two boxes is 27 in terms of volume. However, since the boxes are similar, the scale factor for their linear dimensions (length, width, height) would be the cube root of the volume scale factor:
\[
\text{Linear scale factor} = \sqrt[3]{27} = 3
\]
So, the correct response to the scale factor (in linear dimensions) between the two boxes is:
**3**