  Let $f$ be a $C^{1}$ diffeomorphism on a compact manifold $M$ admitting a
partially hyperbolic splitting $TM=E^{s}\oplus_{\prec} E^{1}\oplus_{\prec}
E^{2}\cdots \oplus_{\prec}E^{l}\oplus_{\prec} E^{u}$ where $E^{s}$ is uniformly
contracting, $E^{u}$ is uniformly expanding and $\dim E^{i}=1,\,1\leq i\leq l.$
We prove an entropy formula w.r.t. the volume growth rate of subspaces in the
tangent bundle:
  $$h_{\rm{top}}(f)=\lim_{n\to+\infty}\frac{1}{n}\log\int\max_{V\subset
T_{x}M}|\det Df_{x}^{n}|_{V}|\,d x.$$
