To determine the correct statement about the two figures based on their volume, we first need to evaluate whether they are similar and then compare the volume ratios based on their dimensions.
- If two figures are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions (lengths, widths, heights, etc.).
- For example, if the ratio of corresponding linear dimensions is \( k : 1 \), then the ratio of volumes will be \( k^3 : 1 \).
To verify the possible answers, you need to know the volumes of both figures.
- If the volumes have a ratio of \( 5 : 1 \), that indicates that if the corresponding linear dimensions are in the ratio of \( \sqrt[3]{5} : 1 \), then the figures are similar.
- If the volumes have a ratio of \( 125 : 1 \), that means the corresponding linear dimensions are in the ratio \( 5 : 1 \), and the figures are also similar.
The options also present a scenario where the figures are not similar if they do not exhibit a consistent volume ratio or if there is no scale factor provided.
Here’s how to interpret the options:
- If you calculate the volumes and confirm they follow a \( k : 1 \) ratio that can be defined as either \( 5 : 1 \) or \( 125 : 1 \), then you can conclude the figures are similar.
- If the calculated volume doesn't match any of the stated ratios or indicates a different ratio without a clear scale factor, you'd select the option stating they are not similar.
Since I cannot view the image to calculate the volumes directly, you would need to determine the ratios based on the actual volume values for a definitive answer. If you can provide the volumes or the dimensions, I can help you calculate the ratios.
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