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 your shown work in a sentinces
Answers
GPT-4o mini
To find the volume of a rectangular pyramid, we use the formula for the volume \( V \):
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, we are given that the base area is \( 200 \) square meters and the height is \( 75 \) meters.
Substituting the values into the formula, we have:
\[
V = \frac{1}{3} \times 200 \, \text{m}^2 \times 75 \, \text{m}
\]
First, we calculate the product of the base area and the height:
\[
200 \times 75 = 15000 \, \text{m}^3
\]
Next, we multiply by \(\frac{1}{3}\):
\[
V = \frac{1}{3} \times 15000 \, \text{m}^3 = 5000 \, \text{m}^3
\]
Thus, the volume of the rectangular pyramid is \( 5000 \) cubic meters.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, we are given that the base area is \( 200 \) square meters and the height is \( 75 \) meters.
Substituting the values into the formula, we have:
\[
V = \frac{1}{3} \times 200 \, \text{m}^2 \times 75 \, \text{m}
\]
First, we calculate the product of the base area and the height:
\[
200 \times 75 = 15000 \, \text{m}^3
\]
Next, we multiply by \(\frac{1}{3}\):
\[
V = \frac{1}{3} \times 15000 \, \text{m}^3 = 5000 \, \text{m}^3
\]
Thus, the volume of the rectangular pyramid is \( 5000 \) cubic meters.