Mass of the core of the sun > mass of the sun?

[h1a8]

I tried calculating the mass of the core of the sun but keep coming up with a number that exceeds the entire mass of the sun. I used http://en.wikipedia.org/wiki/Sun" facts on the sun. It says the core of the sun extends from its center to .2 to .25 times it's radius. I used the number .225 as an average. So this would make the volume of the core to be (.225)^3 or .011 times the sun's total volume. The volume of the Sun is stated to be 1.412e18 km^3 or 1.412e27 m^3. Thus the volume of the core is .011 x 1.412e27 km^3 or 1.608e25 km^3.

Now http://en.wikipedia.org/wiki/Sun#Core" says the density of the core is about 150g/cm^3 or 1.5e5kg/m^3. So since mass = density x volume I get the mass of the core to be:

1.5e5 x 1.608e25 kg = 2.413e30 kg. This exceeds the state mass of the sun (1.9891e30 kg). What is wrong here?

 

[cjl]

That's probably the density at the actual center of the sun, not the average density of the core. Because of that, your mass is coming out too large.

 

[nasu]

In your second link it says that the density of the core varies from 150g/cm3 at the very center to 20 g/cm3 at the edge of the core.
So cjl is right. The average density of the core is significantly lower than 150.

 

[JeffKoch]

I didn't check your numbers, but yes, there isn't a single number for the density of "the core", the density varies with radius. You'd need to integrate over the radial density distribution, and I don't think that's an obvious function since temperature varies with radius too.