Calculus 1 Help: Solving Weight Formula for Distance

[sharingan80]

Okay I had a calculus test and we got it back and I got this question wrong. I tried it again but I can't figure it out.

The weight, w, in kg of an object is inversely proportional to the square of the distance, r, in km, from the center of the earth. Assume a stone of the ground has weight 100 kg and that the diameter of the Earth is approximately 12,756 km. What is the formula of w in terms of r?

I said w=k/r^2 but the question was multiple choice and I wasn't entirely sure so i chose the answer:
w=(100*12756^2)/r^2
but the right answer was
w= (25*12756^2)/r^2

 

[SteamKing]

Why did you use the diameter for r? Where is the center of the Earth in relation to its diameter?

 

[sharingan80]

That's what I'm confused about. I don't know what 12,756 stands for in the equation.

 

[SteamKing]

You don't think it's coincidental that 12756 is also the value given for the diameter of the Earth in kilometers?

Ask yourself, if the diameter of the Earth is 12756 km, how far is the surface of the Earth from the center of the earth?