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 2,190.22 ft.3 2,190.22 ft. cubed 182.52 ft.3 182.25 ft. cubed 3,285.33 ft.3 3,285.33 ft. cubed
Answers
GPT-4o mini
To find the volume of a similar rectangular pyramid given a scale factor, you need to consider that the volume of similar three-dimensional shapes scales with the cube of the scale factor.
If the original pyramid has a volume \( V \) and the scale factor is 23, then the volume \( V' \) of the similar pyramid can be calculated using the formula:
\[
V' = V \times k^3
\]
where \( k \) is the scale factor.
Assuming you have a specific volume for the original pyramid, you would plug that value into the equation along with the scale factor of 23:
\[
V' = V \times 23^3
\]
Calculating \( 23^3 \) gives:
\[
23^3 = 12167
\]
Thus, the new volume would be:
\[
V' = V \times 12167
\]
If you can provide the volume of the original pyramid, I can give you the exact volume of the new pyramid based on the given scale factor. Otherwise, I can't determine which of the options is correct without that information.
If the original pyramid has a volume \( V \) and the scale factor is 23, then the volume \( V' \) of the similar pyramid can be calculated using the formula:
\[
V' = V \times k^3
\]
where \( k \) is the scale factor.
Assuming you have a specific volume for the original pyramid, you would plug that value into the equation along with the scale factor of 23:
\[
V' = V \times 23^3
\]
Calculating \( 23^3 \) gives:
\[
23^3 = 12167
\]
Thus, the new volume would be:
\[
V' = V \times 12167
\]
If you can provide the volume of the original pyramid, I can give you the exact volume of the new pyramid based on the given scale factor. Otherwise, I can't determine which of the options is correct without that information.