Answer
a) $r=7.00\times10^3m$
b) $a=4.50\times10^{-3}\frac{m}{s^2}$
c) $T=7.83\times10^3s$
Work Step by Step
a) $V_S=\frac{4}{3}\pi r^3=(40\times10^3m)(6\times10^3m)(6\times10^3m)$
$r=7.00\times10^{3}m$
b) $m=2.3\times10^3\frac{kg}{m^3}\times1.44\times10^{12}m^3=3.31\times10^{15}kg$
$a=\frac{(6.67\times10^{-11}\frac{Nm^2}{kg^2})(3.31\times10^{15}kg)}{(7.00\times10^{3}m)^2}=4.50\times10^{-3}\frac{m}{s^2}$
c) $T=2\pi\sqrt{\frac{r^3}{Gm}}=2\pi\sqrt{\frac{(7.00\times10^{3}m)^3}{\big(6.67\times10^{-11}\frac{Nm^2}{kg^2}\big)(3.31\times10^{15}kg)}}$
$=7.83\times10^3s$