Question

Please help!

Use spherical coordinates to find the volume of the solid enclosed by the sphere x^2 + y^2 + z^2 = 4a^2 and the planes z=0 to z=a.

Answer 1

I know the limits of integration for dp is 0 to 2a but I have no idea where to go from there.

Answer 2

x=r sin phi cos theta
y=r sin phi sin theta
z= r cos phi
x^2+y^2+z^2=r^2

jacobi =- r^2 sin phi

x^2 + y^2 + z^2 = 4a^2 ---->r^2=4a^2

Answer 3

but I'm not looking for it in terms of r or cylindrical coordinates, just p, phi and theta