Question

the volume of a pyramid can be solved using the formula ( v=\frac{1}{3}bh ). where does the ( \frac{1}{3} ) in the volume formula for a pyramid come from?
the total volume of three prisms is equal to the volume of a pyramid with the same base area and height.
the pyramids base area is effectively reduced by one - third.
the total volume of three pyramids with the same base area and height is equal to the volume of a prism with the same base area and height.
it accounts for the slanted sides of the pyramid.

Explanation:

The volume formula for a prism is \(V = Bh\). Through experiments and geometric reasoning, it has been found that if you take three pyramids with the same base area \(B\) and height \(h\), their combined volume is equal to the volume of a prism with the same base area and height. Mathematically, if \(V_{pyramid}=\frac{1}{3}Bh\), then \(3V_{pyramid}=3\times\frac{1}{3}Bh = Bh=V_{prism}\).

Answer:

The total volume of three pyramids with the same base area and height is equal to the volume of a prism with the same base area and height.