Find a Parametric Representation for the Surface $z = x ^ { 2 } + y ^ { 2 }$

Multiple Choice

Find a parametric representation for the surface $z = x ^ { 2 } + y ^ { 2 }$

A) $x = r \sin \theta$ , $y = r \sin \theta$ , $z = r$

B) $x = r \sin \theta$ , $y = r \sin \theta$ , $z = r ^ { 2 }$
C) $x = r \cos \theta$ , $y = r \cos \theta$ , $z = r$
D) $x = r \cos \theta$ , $y = r \cos \theta$ , $z = r ^ { 2 }$
E) $x = \cos \theta$ , $y = \sin \theta$ , $z = r$
F) $x = \cos \theta$ , $y = \sin \theta$ , $z = r ^ { 2 }$

G) $x = r \cos \theta$ , $y = r \sin \theta$ , $z = r$

H) $x = r \cos \theta$ , $y = r \sin \theta$ , $z = r ^ { 2 }$