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Question
Use the image to answer the question.

An illustration shows a square rectangular pyramid with a side length of 12 meters, a perpendicular height of 10 meters, and a slant height of 11.66 meters. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.
What is the volume of the rectangular pyramid?

(1 point)
Responses

559.68 m3
559.68 m cubed

480 m3
480 m cubed

144 m3
144 m cubed

1,440 m3

Answer 1

To calculate the volume of a rectangular pyramid, you can use the formula:

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

For this pyramid, the base is a square with a side length of 12 meters, and the height is 10 meters.

1. Calculate the base area:
\[
\text{Base Area} = \text{side length}^2 = 12 \, \text{m} \times 12 \, \text{m} = 144 \, \text{m}^2
\]

2. Now, use the volume formula:
\[
\text{Volume} = \frac{1}{3} \times 144 \, \text{m}^2 \times 10 \, \text{m} = \frac{1}{3} \times 1440 \, \text{m}^3 = 480 \, \text{m}^3
\]

Therefore, the volume of the rectangular pyramid is:

\[
\boxed{480 \, \text{m}^3}
\]