To determine which statement about the two figures is true based on their volumes, let's recall the principles of similar figures.
When two figures are similar, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions (such as lengths, widths, or heights).
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If the volume ratio is 125:1, then the scale factor (k) for the linear dimensions can be calculated using the formula: \[ \text{Volume ratio} = k^3 \] Here, \( k^3 = 125 \), which means \( k = \sqrt[3]{125} = 5 \). This indicates that the figures are similar with a linear scale factor of 5:1.
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If the volume ratio is 5:1, it would suggest that the scale factor \( k \) for the linear dimensions is \( k^3 = 5 \), which is incorrect since \( \sqrt[3]{5} \) is not a simple integer.
From these analyses, if indeed the volumes of the two figures are in the ratio 125:1, then the correct conclusion is:
The two figures are similar because the volumes have a ratio of 125:1.
Therefore, the correct statement is:
The two figures are similar because the volumes have a ratio of 125 : 1.