Question

Use the image to answer the question.

A 4-sided pyramid is labeled with a height from the top to base of 28, length of base of 24, and width of base of 22.

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

182.52 ft.3
182.25 ft. cubed

1,460.15 ft.3
1,460.15 ft. cubed

3,285.33 ft.3
3,285.33 ft. cubed

2,190.22 ft.3
2,190.22 ft. cubed
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Answer 1

Original volume = (1/3)(24·22)·28 = (1/3)(528)·28 = 4928 ft^3.

Scale factor = 2/3, so volume scales by (2/3)^3 = 8/27.

New volume = 4928·(8/27) ≈ 1,460.15 ft^3.

Answer: 1,460.15 ft^3.