Problem with the spherical coordinate system

[sagisend]

Hi everyone,
I have a problem where I get a sphere with it's center on (0,0,0.5), how do i convert it to spherical coordiantes when it's center isn't on the center of the axes?
I tried establishing a new varible u=z-0.5 creating a new axes system but it doesn't seem to get me anywhere.. would love some help,

my attempt,getting 0:

thank you.

 

[sagisend]

noticed I eccidentally put 2pi there, apologies.
updated solution with wrong answer.

 

[Dr.Peterson]

Please show the entire actual wording of the problem you are solving. It isn't clear what your goal is, why you want to use spherical coordinates, and so on.

 

[sagisend]

I'm trying to solve the triple integral shown above, I'm using spherical coordinates because it seems like the right way of solving it, with all of the (x^2+y^2+z^2) expressions in the problem. The expression in the [] is the answer for the excercise.
There isn't acutally any additional wording to the problem except for "solve the integral".
anything else unclear?

 

[LCKurtz]

Hi everyone,
I have a problem where I get a sphere with it's center on (0,0,0.5), how do i convert it to spherical coordiantes when it's center isn't on the center of the axes?

In rectangular coordinates your equation is [MATH]x^2+y^2+(z-\frac 1 2)^2=\frac 1 4[/MATH]. Expand it to get [MATH]x^2+y^2+z^2 -z = 0[/MATH]. Now use [MATH]x^2+y^2+z^2=\rho^2[/MATH] and [MATH]z=\rho\cos\phi[/MATH] to wind up with the equation [MATH]\rho =\cos\phi[/MATH] in spherical coordinates. No translation of axes necessary.