Evaluate $\iint_{S} f(x, y, z) d S$ , Where $f(x,y,z)= {x^2}+{y^2}+{z^2}$

Multiple Choice

Evaluate $\iint_{S} f(x, y, z) d S$ , Where $f(x,y,z) = {x^2}+{y^2}+{z^2}$ and S is given by $z=x+y, x^{2}+y^{2} \leq 100$

A) 10,000
B) $10,000 \pi$
C) $10,000 \sqrt { 3 } \pi$
D) $10,000 \sqrt { 2 } \pi$
E) $10,000 \sqrt { 3 }$