Question

.

An illustration shows a 3 D pyramid with a rectangular base. The length, width, and height measurements are labeled. The sides on the front that are visible are shown as solid lines and the sides at the back are shown as dashed lines. The base length is labeled 24 feet and the width is labeled 15 feet. The height is shown as a dotted perpendicular line from the top vertex to the base and is labeled 20 feet. The dotted line continues to the base length to make a right angle.

What is the volume of the pyramid in cubic feet?

(1 point)
ft.3

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

\[
\text{Base Area} = \text{Length} \times \text{Width}
\]

Substituting the given dimensions:

- Length = 24 feet
- Width = 15 feet
- Height = 20 feet

First, calculate the base area:

\[
\text{Base Area} = 24 \, \text{feet} \times 15 \, \text{feet} = 360 \, \text{square feet}
\]

Now, use the volume formula:

\[
V = \frac{1}{3} \times 360 \, \text{square feet} \times 20 \, \text{feet}
\]

Calculating the volume:

\[
V = \frac{1}{3} \times 360 \times 20 = \frac{7200}{3} = 2400 \, \text{cubic feet}
\]

Thus, the volume of the pyramid is:

\[
\boxed{2400} \, \text{ft}^3
\]