  The fully spin polarized composite fermion (CF) Fermi sea at half filled
lowest Landau level has a Fermi wave vector $k^*_{\rm F}=\sqrt{4\pi\rho_e}$,
where $\rho_e$ is the density of electrons or composite fermions, supporting
the notion that the interaction between composite fermions can be treated
perturbatively. Away from $\nu=1/2$, the area is seen to be consistent with
$k^*_{\rm F}=\sqrt{4\pi\rho_e}$ for $\nu<1/2$ but $k^*_{\rm
F}=\sqrt{4\pi\rho_h}$ for $\nu>1/2$, where $\rho_h$ is the density of holes in
the lowest Landau level. This result is consistent with particle-hole symmetry
in the lowest Landau level. We investigate in this article the Fermi wave
vector of the spin-singlet CF Fermi sea (CFFS) at $\nu=1/2$, for which
particle-hole symmetry is not a consideration. Using the microscopic CF theory,
we find that for the spin-singlet CFFS the Fermi wave vectors for up and down
spin CFFSs at $\nu=1/2$ are consistent with $k^{*\uparrow,\downarrow}_{\rm
F}=\sqrt{4\pi\rho^{\uparrow,\downarrow}_e}$, where
$\rho^{\uparrow}_e=\rho^{\downarrow}_e=\rho_e/2$, which implies that the
residual interactions between composite fermions do not cause a
non-perturbative correction for non-fully spin polarized CFFS either. Our
results suggest the natural conjecture that for arbitrary spin polarization the
CF Fermi wave vectors are given by $k^{*\uparrow}_{\rm
F}=\sqrt{4\pi\rho^{\uparrow}_e}$ and $k^{*\downarrow}_{\rm
F}=\sqrt{4\pi\rho^{\downarrow}_e}$.
