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## Homework Statement

Use cylindrical coordinates to find the centroid of the solid.

The solid that is bounded above by the sphere x

^{2}+ y

^{2}+ z

^{2}= 2

and below by z = x

^{2}+ y

^{2}

## Homework Equations

x = rcos(theta)

y= rsin(theta)[/B]

## 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-r

^{2})

^{1/2}and the paraboloid as z = r

^{2}

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 r

^{2}= (2-r

^{2})

^{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.[/B]