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

Find the centroid of the region D, lying above the sphere x^{2}+y^{2}+z^{2}and below the paraboloid z=4-x^{2}-y^{2}.

2. Relevant equations

3. The attempt at a solution

I decided it might be easier to change it to polar coordinates soo I did

M=∫∫∫ dzrdrdθ

where z goes from sqrt(6-r^{2}) to 4-r^{2}

θ goes from 0 to 2∏

then i thought the r would be where the two functions intersect, so i set sqrt(6-r^{2})=4-r^{2}solving for r i got my solutions came out to be sqrt2 and sqrt5, i dont know which one to use because i thought r would go from 0 to either sqrt2 or sqrt5

if some one could help me out i would really appreciate it.. thanks

solving for r i got

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Centroid in three dimensions

**Physics Forums | Science Articles, Homework Help, Discussion**