Question Number 124485 by snipers237 last updated on 03/Dec/20
$${Let}\:{S}^{{n}} =\left\{\left({x}_{\mathrm{0}} ,….,{x}_{{n}} \right)\in\mathbb{R}^{{n}+\mathrm{1}} \:/\:\:\:\underset{{i}=\mathrm{0}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} \:\leqslant\mathrm{1}\right\} \\ $$$${Find}\:\:{Vol}\left({S}^{{n}} \right)\:{for}\:{all}\:{n}\geqslant\mathrm{3} \\ $$