n-ball

$V_{n\text{-ball boundary}}=C_n{r}^{n-1},C_n=n\frac{{\pi }^{n/2}}{\Gamma \left(\frac{n}{2}+1\right)}$

• Desmos Graph

Derivation (in response to 3b1b Video):

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5. $\Gamma \left(\frac{n}{2}+1\right)=\left(\frac{n}{2}\right)!\to C_n=n\frac{{\pi }^{n/2}}{\Gamma \left(\frac{n}{2}+1\right)}$

$V_{n\text{-ball}}=\frac{{\pi }^{n/2}}{\Gamma \left(\frac{n}{2}+1\right)}{r}^n$

• Gamma Function