The volume in the orthogonal group is measured by the Haar measure, which is the up to scaling unique measure that is invariant under the group operation. I consider the usual metric that is induced by the spectral norm |M| = max |Mx| where x ranges over all vectors of length 1 and the vector norm is the Euclidean one. A \delta-ball is the set of all orthogonal matrices that have distance less or equal \delta to a fixed matrix M. Because of the invariance of the Haar measure, for a fixed \delta, all \delta-balls have the same volume.