  We investigate the nodal volume of random hyperspherical harmonics $\lbrace
T_{\ell;d}\rbrace_{\ell\in \mathbb N}$ on the $d$-dimensional unit sphere
($d\ge 2$). We exploit an orthogonal expansion in terms of Laguerre
polynomials; this representation entails a drastic reduction in the
computational complexity and allows to prove \emph{isotropy} for chaotic
components, an issue which was left open in the previous literature. As a
further application, we establish our main result, i.e., variance bounds for
the nodal volume in any dimension; for $d\ge 3$ and as the eigenvalues diverge
(i.e., as $\ell\to +\infty$), we obtain the upper bound $O(\ell^{-(d-2)})$
(that we conjecture to be \emph{sharp}). As a consequence, we show that the
so-called Berry's cancellation phenomenon holds in any dimension: namely, the
nodal variance is one order of magnitude smaller than the variance of the
volume of level sets at any non-zero threshold, in the high-energy limit.
