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

1,440 m3
1,440 m cubed

559.68 m3
559.68 m cubed

480 m3
480 m cubed

144 m3

1 answer

To find the volume of a square pyramid, we use the formula:

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

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

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

The height of the pyramid is given as 10 meters. Plugging the values into the volume formula:

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

Calculating this gives:

\[ \text{Volume} = 480 , \text{m}^3 \]

Thus, the volume of the rectangular pyramid is:

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