Use the image to answer the question.

Question

2 similarly shaped wedge polyhedrons labeled Figure upper A and Figure upper B.

Calculate and compare the volume of the two figures in the image. Choose which statement is true.

(1 point)
Responses

The two figures are similar because the volumes have a ratio of 5 : 1
.
The two figures are similar because the volumes have a ratio of ratio of 5 to 1 .

The two figures are not similar because the volumes are not the same.
The two figures are not similar because the volumes are not the same.

The two figures are similar because the volumes have a ratio of 125 : 1
.
The two figures are similar because the volumes have a ratio of ratio of 125 to 1 .

The two figures are not similar because there is no scale factor stated for the volume.
The two figures are not similar because there is no scale factor stated for the volume.

Answer 1

To determine the similarity of the two wedge polyhedrons and the relationship between their volumes, we need to recall that if two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions (length, width, height, etc.).

If for instance, the ratio of the linear dimensions of Figures A and B is \( k \), then the volume ratio would be \( k^3 \).

Now, let's analyze the provided options:

1. The two figures are similar because the volumes have a ratio of 5 : 1.
2. The two figures are similar because the volumes have a ratio of 5 to 1.
3. The two figures are not similar because the volumes are not the same.
4. The two figures are similar because the volumes have a ratio of 125 : 1.
5. The two figures are similar because the volumes have a ratio of 125 to 1.
6. The two figures are not similar because there is no scale factor stated for the volume.

Without specific volume measurements or a clear ratio of corresponding linear dimensions, we cannot definitively determine which statements are true based strictly on the information provided.

However, if it were established that the volumes have a ratio of \( 125 : 1 \), it would imply that the linear dimensions have a ratio of \( 5 : 1 \), because \( 5^3 = 125 \).

Thus, if you have information confirming a volume ratio of \( 125 : 1 \) or \( 5 : 1 \) seeming accurate based on corresponding dimensions, the correct answer would be one of the statements indicating that they are similar.

If you don't have such specifics, then option 6 could also be appropriate since it states there's no scale factor provided.

With that in mind, the most appropriate response based on a presumed volume ratio of \( 125 : 1 \) would be one of the statements indicating similarity, specifically:

• "The two figures are similar because the volumes have a ratio of 125 : 1."

If you find that the ratio is indeed \( 5:1 \) on measure, the first two options would be correct in context. Please infer based on the exact volume or dimensional comparisons given in the image.