[Physics] Simple Question I need assistance with

I can not, for the life of me, get my head around this physics question i've been assigned. Was wondering if somebody could help me with the answer and explain how they got there, would be extremely appreciated!


'You are a geologist assigned to estimate the density of the Earth. You know that density is given by: *=m / V. You need to first find the volume (V) of the Earth, which can be found by the equation: g=G x m/r2. You are given the following values: G=6.67 x 10-11Nm2kg-2, m=5.97 x 1024 kg and g=9.81 ms-2. Calculate the radius of the Earth and then the volume of the Earth. Assume that the Earth is perfect spherical shape and find its surface area.'

 

They give you the equation:

g = G*m/r^2

solving for r, we get

r = sqrt(G*m/g)

and plugging in the values we are given,

r = sqrt(6.67e-11*5.97e24/9.81) = 6.37e6 m

V = 4/3*pi*r^3 = 4/3*pi*(6.37e6)^3 = 1.08e21 m^3

Solving for density,

density = m/V = 5.97e24/1.08e21 = 5.51e3 kg/m^3

Should convert that to whatever units necessary

 

Thanks so much, really greatful. The way it was worded kept tripping my brain up

 

Good job Meteor. Gonna close this up since it's answered.