To determine if the two figures are similar and to compare their volumes, you would typically look at the ratio of their corresponding linear dimensions, such as heights or lengths. If the two figures are similar, the ratio of their volumes is related to the ratio of their corresponding linear dimensions cubed.
For instance, if the ratio of the linear dimensions of two similar figures is \( a : b \), then the ratio of their volumes will be \( a^3 : b^3 \).
If the statement refers to a ratio of volumes of 125:1, it implies that:
\[ \frac{V_1}{V_2} = \frac{125}{1} \]
Now, since \( 125 \) is \( 5^3 \), this suggests that the ratio of the linear dimensions would be:
\[ \sqrt[3]{125 : 1} = \sqrt[3]{125}/\sqrt[3]{1} = 5 : 1 \]
Thus, if the two figures have a volume ratio of 125:1, they must indeed be similar figures, with their corresponding lengths in the ratio \( 5:1 \).
If the statement claims that the figures are similar because the volumes have a ratio of \( 125 : 1 \), then that statement is true.
Therefore, the correct conclusion is:
The two figures are similar because the volumes have a ratio of 125 : 1.