The X+Y+Z=1 in the first octant looks like the face of a pyramid,
when projected on the XY plane it will look like a filled triangle.
The R looks like a quarter of a ball, so they aren't the same.
To solve the (r,t) surface of the triangle is not so simple, so I won't do it unless you say this is what you want.
Yuwie.com | invite friends. hang out. get paid.