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

2,190.22 ft.3
2,190.22 ft. cubed

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

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

182.52 ft.3

Answer 1

Interpret the scale factor as 2/3. Original volume = (1/3)(24)(22)(28) = 4,928 ft^3. Volume scales by (2/3)^3 = 8/27, so new volume = 4,928*(8/27) ≈ 1,460.15 ft^3.

Answer: 1,460.15 ft^3.