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

3
3

2
2

12
1
2
Start Fraction 1 over 2 End Fraction

Answer 1

To find the scale factor between the two similar boxes, you can compare their volumes.

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

To find the scale factor in volume, you can use the formula:

\[
\text{Scale Factor} = \frac{\text{Volume of Larger Box}}{\text{Volume of Smaller Box}} = \frac{648}{24}
\]

Calculating this gives:

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

The relationship between the volumes of similar figures is the cube of the scale factor of their corresponding linear dimensions. Thus, if \(k\) is the scale factor in linear dimensions, then:

\[
k^3 = 27
\]

To find \(k\), we take the cube root:

\[
k = \sqrt[3]{27} = 3
\]

Therefore, the scale factor between the linear dimensions of the two boxes is \(3\).

**Final Answer:** The scale factor is \(3\).