# Total Mass; Triple Integrals

1. Nov 9, 2008

### withthemotive

1. The problem statement, all variables and given/known data

A lamina occupies the part of the disk x^2 + y^2 ≤ 16 in the first quadrant and the density at each point is given by the function ρ(x,y) = 2(x^2+y^2) .

What is the total mass? Where is the center of mass? (Once I solve total mass I can solve the center by myself.)

3. The attempt at a solution
Total Mass:

I thought it might be easier to solve if I translate this into cylindrical coordinates, so therefore {0≤ r≤ 4, 0≤theta≤ pi/2, 0≤ z≤ 16-r^2}.

I solved this through triple integrals in the order of (rdzdthetadr) and ended up with an answer of (1024/3)*pi, but I'm being told this is incorrect.

2. Nov 9, 2008

### gabbagabbahey

This seems more like a 2D problem than a 3D problem to me...why are you saying that z goes from zero to 16-r^2?

3. Nov 9, 2008

### HallsofIvy

Staff Emeritus
No, this problem is two dimensional. There is no "z". Just use polar coordinates!

4. Nov 9, 2008

### withthemotive

Thanks. I debated on doing it only in 2-D, but turned the idea down. Thanks for clearing that up.

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