解：$(1)$已知$V_0=300\ \mathrm {mL}=300\ \mathrm {cm^3}，$$m_0=318\ \mathrm {g}，$$V=4000\ \mathrm {mL}=4000\ \mathrm {cm^3}，$
血液的密度：$ρ=\frac {m_0}{V_0}=\frac {318\ \mathrm {g}}{300\ \mathrm {cm^3}}=1.06\ \mathrm {g/cm^3}=1.06×10^3\ \mathrm {kg/m^3}；$
$(2)$由$ρ=\frac {m}{V}$得，成年人体内血液的总质量为：$m=ρV=1.06\ \mathrm {g/cm^3}×4000\ \mathrm {cm^3}=4240\ \mathrm {g}=4.24\ \mathrm {kg}.$
