Converting Coordinate Systems

Bit stuck on converting from Cartesian to Spherical:

Let be the spherical surface defined by , and let .

Using SPs , and with

i) Show

ii) Calculate .

i)Well converting to Spherical, we get , so the scalar product gives:

.

Now we also know that , either from using , or from the definition of SPs.

So substituting this in gives:

Which simplifies to:

I'm just at a bit of a loss where they get their extra from?

ii) Integrating this gives us

Which gives , would this be right?

Thanks in advance for any help