  For $n\geq 25$, we construct a smooth metric $\tilde{g}$ on the standard
$n$-dimensional sphere $\mathbb{S}^n$ such that there exists a sequence of
smooth metrics $\{\tilde{g}_k\}_{k\in\mathbb{N}}$ conformal to $\tilde g$ where
each $\tilde g_k$ has scalar curvature $R_{\tilde{g}_k}\equiv 1$ and their
volumes $\text{Vol}(\mathbb{S}^n,\tilde{g}_k)$ tend to infinity as $k$
approaches infinity.
