Similar Figures and Volume Quick Check 3 of 53 of 5 Items Question Use the image to answer the question. Suppose a similar rectangular pyramid to the one shown has a scale factor of 23 . What would be the volume of the new pyramid? (1 point) Responses 1,460.15 ft.3 1,460.15 ft. cubed 182.52 ft.3 182.25 ft. cubed 3,285.33 ft.3 3,285.33 ft. cubed 2,190.22 ft.3 2,190.22 ft. cubed 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 the volume of a similar rectangular pyramid with a scale factor of \( k = 23 \), we need to use the property of similar solids. The volumes of similar solids are proportional to the cubes of their corresponding linear measurements.

If the volume of the original pyramid is \( V \), then the volume \( V' \) of the new pyramid can be calculated using the formula:

\[ V' = k^3 \times V \]

We need to know the volume \( V \) of the original pyramid to proceed further. Assuming we had that information, we could then substitute \( k \) and \( V \) into the above formula to find the volume of the new pyramid.

However, if you already have the options you provided (1,460.15 ft³, 182.52 ft³, 3,285.33 ft³, 2,190.22 ft³), you would compare each option to the calculated volume \( V' \) based on the original volume.

If you could provide the original volume of the pyramid, I could help calculate the new volume based on that information!