Question

What would be the radius of the earth if it had its actual mass but had the density of nuclei?

Answer 1

Answer:

162.3 m

Explanation:

The mass of the Earth is

$M=5.98\cdot 10^{24} kg$

while the density of nuclei is

$d=3.345\cdot 10^{17}kg/m^3$

So we can find the volume of the Earth if it had this density:

$V=\frac{M}{d}=\frac{5.98\cdot 10^{24}kg}{3.345\cdot 10^{17}kg/m^3}=1.79\cdot 10^{7} m^3$

Assuming the Earth is a perfect sphere, its volume is given by

$V=\frac{4}{3}\pi r^3$

where r is the radius. Solving for r, we find

$r=\sqrt[3]{\frac{3V}{4\pi}}=\sqrt[3]{\frac{3(1.79\cdot 10^7 m^3)}{4\pi}}=162.3 m$