Volume between a cone and a sphere

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I am looking for the volume between a cone : $x^2 + y^2 = 2(95-z)^2$ and a sphere : $(x-100)^2 + (y-100)^2 + (z-150)^2= 125^2$. I want to determine the volume of their intersection.

I tried to change coordinates but I am hesitated between spherical and cylindrical.

I can use some software to make the calculation if necessary.

Arrangement between sphere and cone