so, neverminding the units.
[tex]\bf g=\cfrac{GM}{R^2}\implies R^2=\cfrac{GM}{g}\implies R=\sqrt{\frac{GM}{g}}\quad
\begin{cases}
G=6.67\cdot 10^{-11}\\
M=5.97\cdot 10^{24}\\
g=9.81
\end{cases}
\\\\\\
R=\sqrt{\cfrac{{(6.67\cdot 10^{-11})(5.97\cdot 10^{24})}}{9.81}}
\\\\\\
R=\sqrt{\cfrac{{6.67\cdot 5.97\cdot 10^{13}}}{9.81}}
\\\\\\
R\approx 6371116.97~m\\\\
-------------------------------\\\\
V=\cfrac{4\pi R^3}{3}\implies V=\cfrac{4\pi 40591131498470.95^3}{3}
\\\\\\
V\approx 1083266582306022184268.1~m^3[/tex]
