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Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.

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The ratio of the volume of a pyramid to the volume of a prism with the same base and height is Response area. Because the formula for the volume of a prism is V=Bh, where B is the area of the base and h is the height, the formula for the volume of a pyramid is Response area.

Answer 1

The formula for the volume of a pyramid, V=(1/3)*Bh, is derived from the formula for the volume of a prism, V=Bh, based on the ratio of 1/3, which reflects that a pyramid is a prism that tapers to a point.

Step-by-step explanation:

The derivation of the formula for the volume of a pyramid relates to the volume of a prism with the same base and height. The ratio of the volume of a pyramid to the volume of such a prism is 1/3. That's because a pyramid is essentially a prism that tapers to a point. So, because the formula for the volume of a prism is V=Bh (where B represents the area of the base and h represents the height), by replacing this ratio to the formula of the volume of a prism, the formula for the volume of a pyramid is derived as V= (1/3)*Bh.

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