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

## Comments

Sort by:

TopNewestcan you determine the parts of prismatoid? – Nezthiel Mejos · 1 year, 11 months ago

Log in to reply

– Steven Zheng · 1 year, 11 months ago

What do you mean by determine?Log in to reply