Question

Solve the problem. What is the volume of a rectangular pyramid with a base of 200 square meters and a height of 75 meters? Show your work.(2 points) write it humanly and slightly formal

Answer 1

To find the volume of a rectangular pyramid, we can use the formula for the volume of a pyramid, which is given by:

\[
V = \frac{1}{3} \times B \times h
\]

where:
- \( V \) is the volume,
- \( B \) is the area of the base, and
- \( h \) is the height of the pyramid.

In this case, we are provided with:
- The base area \( B = 200 \) square meters,
- The height \( h = 75 \) meters.

Now, we can substitute these values into the volume formula:

\[
V = \frac{1}{3} \times 200 \, \text{m}^2 \times 75 \, \text{m}
\]

Next, we will perform the multiplication:

\[
V = \frac{1}{3} \times 15000 \, \text{m}^3
\]

Calculating the above gives:

\[
V = 5000 \, \text{m}^3
\]

Thus, the volume of the rectangular pyramid is

\[
\boxed{5000} \, \text{cubic meters}.
\]