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Question Number 124485 by snipers237 last updated on 03/Dec/20

Let S^n ={(x_0 ,....,x_n )∈R^(n+1)  /   Σ_(i=0) ^n x_i ^2  ≤1}  Find  Vol(S^n ) for all n≥3

$${Let}\:{S}^{{n}} =\left\{\left({x}_{\mathrm{0}} ,....,{x}_{{n}} \right)\in\mathbb{R}^{{n}+\mathrm{1}} \:/\:\:\:\underset{{i}=\mathrm{0}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} \:\leqslant\mathrm{1}\right\} \\ $$$${Find}\:\:{Vol}\left({S}^{{n}} \right)\:{for}\:{all}\:{n}\geqslant\mathrm{3} \\ $$

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