Question

A right rectangular pyramid has an altitude of 35 m, a length of 26 m, and a width of 31 m. What is the volume of the pyramid in m3.
?(1 point)
Responses

84,630 m3
84,630 m cubed

28,210 m3
28,210 m cubed

30.67 m3
30.67 m cubed

9,403.33 m3

Answer 1

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

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

The base of the pyramid is a rectangle, so the area \( A \) of the base can be calculated using the formula:

\[
\text{Base Area} = \text{length} \times \text{width}
\]

Given:
- Length \( l = 26 \) m
- Width \( w = 31 \) m
- Height \( h = 35 \) m

First, calculate the base area:

\[
\text{Base Area} = 26 \, \text{m} \times 31 \, \text{m} = 806 \, \text{m}^2
\]

Now, substitute the base area and height into the volume formula:

\[
V = \frac{1}{3} \times 806 \, \text{m}^2 \times 35 \, \text{m}
\]

Calculating:

\[
V = \frac{1}{3} \times 806 \times 35 = \frac{28,210}{3} \, \text{m}^3 \approx 9,403.33 \, \text{m}^3
\]

Thus, the volume of the pyramid is:

\[
\boxed{9,403.33 \, \text{m}^3}
\]