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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

$</code> ... <code>$</code>...<code>."> Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in $</span> ... <span>$ or $</span> ... <span>$ to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestcan you determine the parts of prismatoid?

Log in to reply

What do you mean by determine?

Log in to reply