The average radius of Earth is \(6371 \mathrm{~km}\). Give order-ofmagnitude estimates of what the mass of Earth would be if the planet has the mass density of \((a)\) air \(\left(\approx 1.2 \mathrm{~kg} / \mathrm{m}^{3}\right)\), (b) \(5515 \mathrm{~kg} / \mathrm{m}^{3}\), and \((c)\) an atomic nucleus \(\left(\approx 10^{18} \mathrm{~kg} / \mathrm{m}^{3}\right)\).