Question

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Volume of Pyramids Quick Check
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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

480 m3
480 m cubed

1,440 m3
1,440 m cubed

559.68 m3
559.68 m cubed

144 m3

Answer 1

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

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

In this case, the base of the pyramid is a square with a side length of 12 meters. Therefore, the area of the base is:

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

The height of the pyramid is given as 10 meters. Substituting the base area and height into the volume formula gives:

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

Thus, the volume of the rectangular pyramid is:

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