Multivariable Question

[Hazardus]

Problem:
Find the volume of the smaller wedge cut from a sphere of radius "a" by two planes that intersect along a diameter at an angle of Pi/6.
Question about it:
In class my prof said that the plane Pi/6 is equal to the plane phi = Tan^-1(1/(SqRoot(3)SinTheta)). This is coming from of course spherical coordinates and going to cylindrical coordinates. How do you get from one to the other in this case?!

[HallsofIvy]

I'm not sure WHY you would want to do that! The simplest way to find the volume is to note that pi/6 is (pi/6)/(2pi)= 1/12 of the entire sphere. The volume cut off is 1/12 the volume of the sphere.

"In class my prof said that the plane Pi/6 is equal to the plane phi = Tan^-1(1/(SqRoot(3)SinTheta)). This is coming from of course spherical coordinates and going to cylindrical coordinates. How do you get from one to the other in this case?!"
I have no idea what you mean by this! "the plane pi/6"?? Do you mean the plane corresponding to phi= pi/6? Apparently not since you then give phi= ... And this is most certainly not "coming from spherical coordinates to cylindrical coordinates" since phi is only defined in spherical coordinates.