Find the Area of the Part of the Surface $y = 8 x + z ^ { 2 }$

Multiple Choice

Find the area of the part of the surface $y = 8 x + z ^ { 2 }$ that lies between the planes $x = 0 , x = 4 , z = 0$ , and $z = 1$ . Select the correct answer.

A) $32.5768$
B) $39.7002$
C) $44.7002$
D) $41.7002$
E) $42.7002$