how do you find the radius of a sphere w/ center (3,2,4) and tangent to the xy-plane?

Answer 1

The xy plane is the plane z = 0. The radius is perpendicular to the xy plane and therefore the difference in the z values.

r = 4 - 0 = 4.

The radius is 4.

Answer 2

Because you are tangent to the xy plane, the radius is the distance between the z coordinate of the center and the xy plane - in this case, 4

Answer 3

This is just a 3D version of your circle problem

if the xy plane is a tangent then the z coordinate is zero. The z coordinate of the centre is 4 and so the radius must be 4.