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? L = 22 W = 24 H = 28 (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

Answers

GPT-4o mini
To find the volume of a pyramid, you can use the formula:

\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

For a rectangular pyramid, the base area is calculated as:

\[
\text{Base Area} = \text{Length} \times \text{Width} = L \times W
\]

In this case, we have:

- Length (L) = 22 ft
- Width (W) = 24 ft
- Height (H) = 28 ft

Now, calculate the base area:

\[
\text{Base Area} = 22 \times 24 = 528 \text{ ft}^2
\]

Next, calculate the volume of the original pyramid:

\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 528 \times 28
\]

Calculating further:

\[
\text{Volume} = \frac{1}{3} \times 14784 = 4928 \text{ ft}^3
\]

Now, since the new pyramid is similar to the original one with a scale factor of 23, the volume of the new pyramid is scaled by the cube of the scale factor:

\[
\text{New Volume} = \text{Original Volume} \times (\text{Scale Factor})^3 = 4928 \times 23^3
\]

Calculating \(23^3\):

\[
23^3 = 12167
\]

Now calculate the new volume:

\[
\text{New Volume} = 4928 \times 12167
\]

Calculating this gives:

\[
\text{New Volume} = 600,812.56 \text{ ft}^3
\]

None of the responses given seem to match this answer, so please double-check the scale factor or dimensions if they were meant to be different. If everything provided is correct, you may need to provide additional context to align with the responses given, as my calculations show a substantially larger volume.