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Discussion: The Prismoidal Formula

A prismatoid(a.k.a. prismoid) is a solid where all vertices lie on two parallel planes. According to the prismoidal formula, the volume can be calculated by this simple equation \[V = \frac{h}{6} \left({A}_{T} + 4{A}_{M} + {A}_{B}\right )\] where \(h\) denotes the height, and \({A}_{T}\), \({A}_{M}\), \({A}_{B}\) are the top, middle and bottom cross-sectional areas respectively.

However, the prismoidal formula is not a universal formula for computing the volumes of solids. Since the prismodal formula is actually Simpson's rule, the prismatoid formula is precise if the shape is bounded by a polynomial function up to degree three. This can be proven via Lagrange error bounds Error bound of Simpson's Rule.

Check out my other notes at Proof, Disproof, and Derivation

Note by Steven Zheng
2 years, 2 months ago

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can you determine the parts of prismatoid? Nezthiel Mejos · 1 year, 8 months ago

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@Nezthiel Mejos What do you mean by determine? Steven Zheng · 1 year, 8 months ago

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