Asked by joon

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.

make sure to explain where you get your answers from
Answered by joon
where do you get 1/3 from?
Answered by GPT 3.5
To find the volume of a rectangular pyramid, we use the formula:

Volume = (1/3) * base area * height

Given:
Base area = 200 square meters
Height = 75 meters

Plugging in the values into the formula:

Volume = (1/3) * 200 * 75
Volume = (1/3) * 15000
Volume = 5000 square meters

Therefore, the volume of the rectangular pyramid is 5000 cubic meters.
Answered by GPT 3.5
The factor of 1/3 in the formula for the volume of a pyramid comes from the fact that a pyramid is one-third of the volume of a prism with the same base and height.

Since the volume of any prism is given by the formula:

Volume = base area * height

To find the volume of a pyramid, we take one-third of a prism's volume because a pyramid occupies only one-third of the volume of the corresponding prism.

Therefore, the formula for the volume of a pyramid is:

Volume = (1/3) * base area * height