## Spherical Coordinates of an Ice Cream Cone

For a homogeneous Ice-Cream Cone, given by the spherical coordinates phi=pi/4 (the bottom part) and rho=cos(phi) (the top part), I need to find the Center of Mass and the Surface Area using integrals.

...I think I'm mostly confused how to find the surface area, I'm getting it confused with the volume...

Any help or insight on this problem would be most appreciated!!