Answer
$$(48 \sqrt 2-12)\pi $$
Work Step by Step
We know that $$ div F=\dfrac{\partial P}{\partial x}i+\dfrac{\partial Q}{\partial y}j $$
From the given equation, we have $$ Flux =\iiint_{o} 15x^2+15y^2+15z^2 \space dA \\=\nabla \cdot F \\= \int_{0}^{2 \pi}\int_{0}^{\pi}\int_{0}^{\sqrt 2} (15 \rho^2) \times (\rho^2 \sin \phi) d\rho \space d \phi \space d\theta \\=\int_{0}^{2 \pi}(24 \sqrt 2-6) \space d\theta \\=(48 \sqrt 2-12)\pi $$
