Question
What is the volume of the rectangular pyramid?
(1 point)
Responses
144 m3
144 m cubed
480 m3
480 m cubed
559.68 m3
559.68 m cubed
1,440 m3
Width: 12 m
Length: 12m
Height: 10 m
Triangular face: 11.66 m
(1 point)
Responses
144 m3
144 m cubed
480 m3
480 m cubed
559.68 m3
559.68 m cubed
1,440 m3
Width: 12 m
Length: 12m
Height: 10 m
Triangular face: 11.66 m
Answers
GPT-4o mini
The volume \( V \) of a rectangular pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base is a rectangle with a length of 12 m and a width of 12 m. Therefore, the area of the base \( A \) is:
\[
A = \text{Length} \times \text{Width} = 12 \, \text{m} \times 12 \, \text{m} = 144 \, \text{m}^{2}
\]
The height of the pyramid is given as 10 m.
Now, we can plug these values into the volume formula:
\[
V = \frac{1}{3} \times 144 \, \text{m}^{2} \times 10 \, \text{m}
\]
\[
V = \frac{1}{3} \times 1440 \, \text{m}^{3}
\]
\[
V = 480 \, \text{m}^{3}
\]
Thus, the volume of the rectangular pyramid is **480 m³**.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base is a rectangle with a length of 12 m and a width of 12 m. Therefore, the area of the base \( A \) is:
\[
A = \text{Length} \times \text{Width} = 12 \, \text{m} \times 12 \, \text{m} = 144 \, \text{m}^{2}
\]
The height of the pyramid is given as 10 m.
Now, we can plug these values into the volume formula:
\[
V = \frac{1}{3} \times 144 \, \text{m}^{2} \times 10 \, \text{m}
\]
\[
V = \frac{1}{3} \times 1440 \, \text{m}^{3}
\]
\[
V = 480 \, \text{m}^{3}
\]
Thus, the volume of the rectangular pyramid is **480 m³**.