Question

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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

1,440 m3
1,440 m cubed

480 m3
480 m cubed

559.68 m3
559.68 m cubed

144 m3
144 m cubed
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Answer 1

To find the volume of a square pyramid, the formula is:

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

Given:

- The side length (base length) of the square pyramid is 12 meters.
- The height of the pyramid (perpendicular height) is 10 meters.

First, we calculate the base area:

\[
\text{Base Area} = \text{side length}^2 = 12 \, \text{m} \times 12 \, \text{m} = 144 \, \text{m}^2
\]

Next, we apply the volume formula:

\[
\text{Volume} = \frac{1}{3} \times 144 \, \text{m}^2 \times 10 \, \text{m}
\]
\[
\text{Volume} = \frac{1}{3} \times 1440 \, \text{m}^3
\]
\[
\text{Volume} = 480 \, \text{m}^3
\]

Thus, the volume of the rectangular pyramid is:

**480 m³**