First , calculate the numinator :
Since it is uniform , we may neglect the density .
Oh i made a mistake , i thought that is a part of a sphere ...
The function should be
Problem: Determine the z-coordinate of the centroid of the solid generated by revolving the quarter-circular area thorugh 90 degress about the z-axis.
I tried to calculate the volume of the solid. I got it to be
I have some trouble setting up the sum of moments integral, that is
I tried to use a horizontal strip as differential element:
But I also need thickness, right? expressed in terms of z