Finding mass of sphere with density

[burton4]

http://tgnot.com/triple_integral_sphere.jpg

A solid ball of radius a has density given by (2a-p) where p = sqrt(x^2 + y^2 + z^2). Determine its mass.

a) I think it's properly setup by converting to spherical, still iffy if (2a-p)=(2p-p)=p

b) What did I just find and how do I then get mass?Thanks-a-centillion if you reply, this isn't homework, but is part of a practice midterm.

 

[Dick]

(2a-p)=p is only true where a=p. That's on the outside of your sphere. On the inside it's just (2a-p). Integrate that.

 

[1919]

If you take the integral of (2a-p) it should work.
Remember the mass is the integral of the density so the boundaries are p^2sin(phi)dp(dtheta)(dphi)
The boundary conditions are:
phi: 0... pi
theta: 0...2pi
p: 0...a

So, triple integral(2a-p)p^2sinphi(dpdthetadphi)

Sorry, I don't know how to make symbols on here yet but hope this helps!