Answer
$\dfrac{256\pi}{3}$
Work Step by Step
Divergence Theorem: $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV $
$div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}=0+1+0=1$
$\iiint_E div F dV$ shows the volume of the region $E$ and the region $E$ lies inside a sphere with radius $4$.
Volume of the region E;$=\dfrac{4\pi(4)^3}{3}=\dfrac{256\pi}{3}$
Hence, we get $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV =\dfrac{256\pi}{3}$
