(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

After determining the average density of Mercury as 5.43 x 10^3(kg/m3), you may calculate the size of Mercury's core. Assume Mercury consists of a core and a mantle+crust, with core composition being similar to Earth (7,800(kg/m3)). From space missions and studying meteorites we know that the density of the mantle+crust is about 2,600 (kg/m3). Calculate the radius of Mercury, using the total radius of Mercury from NASA.

2. Relevant equations

My problem is that I don't know what equation to use. I am attempting a geophysics course in university after having finished high school physics three years ago, which I did by correspondence, teaching myself out of a book! This is all a little new to me; I still have to look up the equations for volume on Wikipedia.

3. The attempt at a solution

I spoke to my professor about the problem. We determined that the known variables are:

Density of Mercury: 5.43 x 10^3 (kg/m3)

Density of Mercury's Core: 7,800 (kg/m3)

Density of Mercury's Mantle: 2,600 (kg/m3)

Radius of Mercury: 2,439,700 m

The unknown is the radius. He told me that the equation I will need to solve the problem will involve my known variables. (I wrongly assumed I could look something up very simply.) I have thought about using v=4/3(pi)r^3, but I don't know the volume of the core. I thought about calculating the volume of the mantle and subtracting it from the total volume of Mercury to find the volume of the core, but I don't think I have enough information to do that. I've considered using a ratio, but any ratio I can think of, I don't have enough information for. Can anyone point me in the right direction?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Radius of Mercury's Core

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