(3) Cuts meeting at the intersection of a "T" interior to the cake.

Here we see from our diagram that the angle q (theta) is the variable to consider. We make the two line cuts AB and PC.

We seek theta such that pieces BPC, APC, and APBD each have area 1/3 Pi R^2.

Clearly theta will be less than Pi/2.

And we check to see if the area of region BPC is 1/3 Pi R^2 = 1.047 R^2. It is!

And now for the top area above the T. We see it too is 1/3 Pi R^2.