The density of a carbon nucleus from literature is equal to 2.01×10¹⁵ g/cm³. We will have to equate the density of the Earth to this value. First, let's find the mass of the Earth from the given data:
Volume of Earth = 4/3π(6.4×10³ km * 100,000 cm/1 km)³
Volume = 1.098×10²⁷ cm³
Mass of Earth = 5.5 g/cm³ * 1.098×10²⁷ cm³
Mass of Earth = 6.039×10²⁷ g
Then, we equate this with the density of carbon nucleus.
2.01×10¹⁵ g/cm³ = 6.039×10²⁷ g/V
V = 3×10¹² cm³
Let's equate this to the volume of a sphere of the Earth:
V = 3×10¹² cm³ = 4/3*πr³
r = 40.18 cm
The radius of the Earth should be reduced to 40.18 cm.
