triple integral-spherical coordinates

mcc123pa

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

tiny-tim

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 … ?

Matterwave

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).

tiny-tim

Hi Matterwave!

No, it's ok …

engineers do it the other way round!

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!

LCKurtz

That's right. But it is "pi", not "pie".

mcc123pa

Thanks LCKurtz!! I'll remember it's pi not pie from now on...thanks for the tip!!