Question

Volume of Pyramids Quick Check
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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)

Answer 1

The volume \( V \) of a pyramid can be calculated using the formula:

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

For a right rectangular pyramid, the base area can be calculated as:

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

Given:
- Length = 26 m
- Width = 31 m
- Height (altitude) = 35 m

First, calculate the base area:

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

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

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

Calculating this gives:

\[
V = \frac{1}{3} \times 806 \times 35 = \frac{28210}{3} \approx 9403.33 \, \text{m}^3
\]

Thus, the volume of the pyramid is approximately \( 9403.33 \, \text{m}^3 \).