Question

Similar Figures and Volume Quick Check 1 of 51 of 5 Items Question Use the image to answer the question. Calculate and compare the volume of the two figures in the image. Choose which statement is true. (1 point) Responses 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. 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 . Skip to navigation page 14 of 14 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine whether the two figures are similar based on their volumes, we need to know the specific volumes of each figure and the relationship between these volumes.

1. Understanding Similar Figures:

   • Two figures are similar if their corresponding dimensions (lengths, heights, etc.) are in proportion.
   • The volume ratio of similar figures is equal to the cube of the ratio of their corresponding linear dimensions.

2. Volume Ratios:

   • If the volume of the larger figure is $V_1$ and that of the smaller figure is $V_2$, then the ratio of their volumes is $\frac{V_1}{V_2}$.
   • If the ratio of the volume is $125:1$, then the ratio of their corresponding linear dimensions is $\sqrt[3]{125}:1$, which simplifies to $5:1$.
   • Therefore, if the volume ratio is $125:1$, the linear dimension ratio is $5:1$.

3. Identifying the Correct Statement:

   • If the figures have a volume ratio of $125:1$, they are similar, as their linear dimensions have a ratio of $5:1$.
   • The other options suggest that the figures do not maintain similarity based on equal volumes or lack of a stated scale factor, both of which are incorrect if the ratio is $125:1$.

Based on these points, the correct statement would be: The two figures are similar because the volumes have a ratio of 125 : 1.