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

144 m3
144 m cubed

1,440 m3
1,440 m cubed

480 m3

1 answer

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

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

Given the side length of the base (which is square) is 12 meters, the base area can be calculated as:

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

The height of the pyramid is given as 10 meters. Now we can substitute these values into the volume formula:

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

Therefore, the volume of the rectangular pyramid is:

480 m³