What is the mass of Uranus outside the core

If the core of Uranus has a radius twice that of planet Earth and an average density of 8000 kg/m^3, what is the mass of Uranus outside the core?

This problem requires you to know the total mass and radius of Uranus and the radius of the Earth (from your textbook or by asking the Internet, not intuitively). The second major thing you need to know is the formula for the volume of a sphere:

V = (4/3)πr^3

The value my physics textbook gives me for the mass of Uranus is 8.68 x 10^25 kg. Uranus' radius is 2.33 x 10^7 m and Earth's radius is 6.37 x 10^6 m.

First, you have to find the mass of Uranus' core. Rewriting the density equation ρ = m/V to solve for mass gives you m = ρV. For a sphere:

m = (4/3)πρr^3

m = (4/3)π x (8 x 10^3 kg/m^3) x (2 x 6.37 x 10^6 m)^3

m = (32/3)π x (10^3 kg/m^3) x (2.07 x 10^21 m^3)

m = (32/3)π x (2.07 x 10^24 kg)

m = 6.94 x 10^25 kg

The answer is then Uranus' total mass minus its core mass.

M - m = (8.68 x 10^25 kg) - (6.94 x 10^25 kg) = 1.74 x 10^25 kg

1/3 of earth's total mass is the core. The core is about the size of mars.