Answer:
162.3 m
Explanation:
The mass of the Earth is
[tex]M=5.98\cdot 10^{24} kg[/tex]
while the density of nuclei is
[tex]d=3.345\cdot 10^{17}kg/m^3[/tex]
So we can find the volume of the Earth if it had this density:
[tex]V=\frac{M}{d}=\frac{5.98\cdot 10^{24}kg}{3.345\cdot 10^{17}kg/m^3}=1.79\cdot 10^{7} m^3[/tex]
Assuming the Earth is a perfect sphere, its volume is given by
[tex]V=\frac{4}{3}\pi r^3[/tex]
where r is the radius. Solving for r, we find
[tex]r=\sqrt[3]{\frac{3V}{4\pi}}=\sqrt[3]{\frac{3(1.79\cdot 10^7 m^3)}{4\pi}}=162.3 m[/tex]
