The mass of tithe earth is 5.98x10^24kg, and its radius is 6.38x10^8m. Compute the density of the earth, using powers-of-ten notation and the correct number of significant figures.
+14995 The mass of tithe earth is 5.98x10^24kg, and its radius is 6.38x10^8m. Compute the density of the earth, using powers-of-ten notation and the correct number of significant figures.
Hello Guest!
The radius of our earth is \(6393km \approx 6.39 \times10 ^ 6m\).
\(Density=\dfrac{mass}{volume}\)
\(\rho=\dfrac{m}{V}=\dfrac{5.98\cdot 10^{24}\cdot kg}{\frac{4}{3}\pi\cdot 6.39^3\cdot (10^6)^3\cdot m^3}\times\dfrac{m^3}{10^6\cdot cm^3}\times\dfrac{10^3\cdot g}{kg}\\ =\dfrac{3\cdot 5.98}{4\cdot 6.39^3\cdot \pi}\times\dfrac{10^{24}\cdot 10^3}{10^{18}\cdot 10^6}\times\dfrac{g}{cm^3}\color{blue}\approx5.47g/cm^3\)
!
+37146 Using different units:
m / v = density
5.98* 10^24 kg / 4/3 pi (6.38* 10^8)^3 = .0054973 kg/m3 =5.49 *10-3 kg/m3
