To determine which statement is true, we can analyze the concept of similarity in geometric figures, particularly polyhedrons.
When two polyhedrons are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions (such as height, width, or base length). If the linear dimensions have a ratio of a : b, then the volumes will have a ratio of \( a^3 : b^3 \).
If we assume that the two figures are indeed similar based on the given options, we would need to establish a scale factor for their dimensions.
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If the volume ratio is stated as 125 : 1, that implies that the scale factor for the linear dimensions is \( 5 : 1 \) since \( 5^3 = 125 \). This means that the first figure is 5 times larger than the second in terms of linear dimensions.
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If the volume ratio is stated as 5 : 1, it would imply a scale factor of roughly \( \sqrt[3]{5} : 1 \), which indicates a much smaller relationship between the dimensions, but this doesn't correspond to the ratio mentioned in the problem.
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Without a stated scale factor or specific dimensions for the two figures, we cannot directly compare the volumes or confirm similarity through numerical values, leading to the conclusion that they cannot be assessed as similar based solely on volume comparison.
Given these interpretations, the most accurate response based on volume and similarity principles would be:
The two figures are similar because the volumes have a ratio of 125 : 1.
This indicates that they have a scale factor of 5 : 1 in their linear dimensions, maintaining the concept of geometric similarity.
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