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Rule

Volume of a Prism

Consider a prism with a base area

B

and height

h .

The volume of the prism is calculated by multiplying the base's area by its height.

$V = B h$

By Cavalieri's principle, this formula holds true for all types of prisms, including skewed ones.

Proof

Informal Justification

Recall that the volume of a solid is the measure of the amount of space inside the solid. Note that the top and bottom faces of the prism are always the same and parallel to each other.

Additionally, the prism is, so to speak, filled with identical base areas that are stacked on top of each other to the height of the prism.

This means that the volume of the prism can be calculated as the sum of all these base areas. The number of bases is equal to the height of the prism. Therefore, the volume of a prism equals the product of its base area and height.

V = h B + B + B + \dots + B + B ⇓ V = B \cdot h

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Proof