Higher Dimensions

First, we compute the volume of an n-dimensional ball \(B^n(r)\) of radius r in \({\mathbb {R}}^n\) , and we prove that for every fixed \(r>0\) , the volume of the n-dimensional ball tends to 0 as n tends to \(\infty \) . How many unit balls in \({\mathbb {R}}^n\) can touch \(B^n(r)\) simultaneously?