Answer
(a) $r = 1.65\times 10^4~km$
(b) The radius is 2.59 times the Earth's radius.
Work Step by Step
We can use $5.97\times 10^{24}~kg$ as the Earth's mass.
We can use $6.38\times 10^6~m$ as the Earth's radius.
(a) $\rho = \frac{mass}{volume} = \frac{(5.5)(5.97\times 10^{24}~kg)}{\frac{4}{3}\pi r^3} = 1.76\times 10^3~kg/m^3$
$r^3 = \frac{(3)(5.5)(5.97\times 10^{24}~kg)}{(4\pi)(1.76\times 10^3~kg/m^3)} = 4.454\times 10^{21}~m^3$
$r = 1.65\times 10^7~m = 1.65\times 10^4~km$
(b) We can convert this radius to a multiple of Earth's radius.
$r = \frac{1.65\times 10^4~km}{6.38\times 10^3~km} = 2.59$
The radius is 2.59 times the Earth's radius.
