Two Pieces of a Fence (AR Modeling Challenge)

Using only 2 surface equations (with domain restrictions), how can we reconstruct what is seen in the screencast below? [br][br][b]Clues:[/b][br][br]1) The vertex of the [b][color=#1e84cc]blue paraboloid of revolution[/color][/b] is (3, 0, 5).[br][br]2) The point [math]\left(4,-\frac{2\sqrt{3}}{3},4\right)[/math] lies on the [b][color=#1e84cc]paraboloid of revolution[/color][/b]. [br][br]3) The radius of the circular opening at the bottom of the [b][color=#1e84cc]paraboloid of revolution[/color][/b] = [math]\sqrt{5}[/math]. [br][br]4) The [b][color=#ff00ff]pink surface[/color][/b] is [b][color=#ff00ff]half a cylinder[/color][/b]. This [color=#ff00ff][b]cylinder [/b][/color]has a radius = 2. [br][br]5) The axis of the [b][color=#ff00ff]cylinder[/color][/b] is can be found by translating the xAxis by the vector <0, 0, -2>. [br]
Quick Demo

Information: Two Pieces of a Fence (AR Modeling Challenge)