1. The problem statement, all variables and given/known data Use cylindrical coordinates to find the centroid of the solid. The solid that is bounded above by the sphere x2 + y2 + z2 = 2 and below by z = x2 + y2 2. Relevant equations x = rcos(theta) y= rsin(theta) 3. The attempt at a solution I am having trouble trying to find the limits of integration for r. I have been able to get the sphere in terms of r as z = (2-r2)1/2 and the paraboloid as z = r2 I understand that in cylindrical coordinates the region is occupied from 0<theta<2pi and r originates from origin n to the uppermost part of the sphere. I also found that when you equate both surface z equations. you get r2 = (2-r2)1/2 . Solving for r you get radical 2 and 1. r being the furthest distance would then have the upper limit of 1. I'm not sure if this is the correct method of solving.