Question

Select One

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 inches3. Compare the volumes and determine the scale factor between the two boxes.(1 point) Responses 1 1 3 3 12 Start Fraction 1 over 2 End Fraction 2

Answer 1

To find the scale factor between the two boxes, we can compare their volumes directly.

The volume of the larger box is 648 inches³, and the volume of the smaller box is 24 inches³. To find the scale factor, we take the ratio of the volumes:

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

Calculating the division:

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

The scale factor for the linear dimensions between two similar shapes can be found by taking the cube root of the scale factor of the volumes, since volume scales with the cube of the linear dimensions.

So, we find the cube root of 27:

\[
\text{Linear Scale Factor} = \sqrt[3]{27} = 3
\]

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