A fluid having density $f(x, y, z) = x^{2} + 2y^{2} + z^{2}$ flows with velocity $v(x, y, z) = x^{2}i + xy^{2}j + zk$. Determine the rate of mass flow through the sphere $ρ = 1$ in the outward direction
I am unsure of where to start on this problem. I see outward direction, which makes me think use divergence formula but $f(x, y, z)$ is a scalar function, not a vector field.
Hint: What is the definition of rate of mass flow?