  We continue the study of 3d ${\mathcal N}=2$ Chern-Simons (CS) quiver gauge
theories on $\Sigma_{\mathfrak{g}}\times S^1$. Using localization results, we
compute the twisted index of recently constructed SCFTs in the large rank
limit. According to AdS/CFT correspondence, this field theory computation gives
a prediction for two quantities corresponding to their holographic duals: the
volumes of certain 7-dimensional Sasaki-Einstein manifolds and the entropy of
black holes in $\text{AdS}_4\times Y_7$.
