Answer
$2 \pi$
Work Step by Step
$div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}=4 \sqrt {x^2+y^2+z^2}$
Now, we have
$Flux=4 \times \int_{0}^{2 \pi}\int_0^{\pi/2} \int_{0}^{1} 4 \sqrt {x^2+y^2+z^2} dV$
$=4 \times \int_{0}^{2 \pi}\int_0^{\pi/2} \int_{0}^{1} \sqrt{\rho^2} \rho^2 \sin \phi d \rho d\phi d \theta$
$=4 \times \int_{0}^{2 \pi} d \theta \times \int_0^{\pi/2} \sin \phi d\phi \times \int_{0}^{1} \rho^2 d \rho$
$=4 (2 \pi) \times (-\cos \phi)_0^{\pi/2} \times [\dfrac{\rho^4}{4}]_0^1$
$=2 \pi$
