## triple integral-spherical coordinates

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

Here is exactly what the problem says:
Let T be a solid of density one that lies below x^2+y^2+z^2=9 and above the XY-plane.
a) Use the triple integral to find its mass.
b) Find the centroid.

2. Relevant equations

I believe that this should be an integral in spherical coordinates. I know the relevant equation is p^2sin(phi) dpd(phi)d(theta).

3. The attempt at a solution

Obviously the first step is to set up the triple integral in spherical coordinates. I set x^2+y^2+z^2=9 and changed it to p^2=9. This left me with the limits of integration for p being from 0 to 3. I know that theta's integral is normally from 0 to 2(pie). I have no clue how to solve for the 'phi' limits and obviously I can't complete the problem until I do. Please advise as soon as possible what I should do. Thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor hi mcc123pa! welcome to pf! (have a theta: θ and a phi: φ and a pi: π and try using the X2 icon just above the Reply box ) φ is the latitude (or co-latitude), and it goes from the pole to the equator, so that's … ?
 This is not the usual definition of φ in spherical coordinates. Usually φ is the polar coordinate (analogous to longitude, but just starting at 0 and ending at 360, instead of being split between west and east), and θ is the co-latitude (90 degrees-latitude, with latitudes being negative below the x-y plane).

Blog Entries: 27
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Homework Help

## triple integral-spherical coordinates

Hi Matterwave!

No, it's ok …
engineers do it the other way round!
 Hi everyone- thanks for the help so far.... tiny-tim, From the pole to the equator, that's pie/2. Is that correct? So I guess in the case that is correct, the limits are as follows: p = from 0 to 3 phi = from 0 to (pie)/2 theta = from 0 to (2pie) Please confirm if I have this right everyone. Thanks for your help!

Recognitions:
Gold Member
Homework Help
 Quote by mcc123pa Hi everyone- thanks for the help so far.... tiny-tim, From the pole to the equator, that's pie/2. Is that correct? So I guess in the case that is correct, the limits are as follows: p = from 0 to 3 phi = from 0 to (pie)/2 theta = from 0 to (2pie) Please confirm if I have this right everyone. Thanks for your help!
That's right. But it is "pi", not "pie".
 Thanks LCKurtz!! I'll remember it's pi not pie from now on...thanks for the tip!!