Using Divergence Theorem to evaluate the surface integral

Question

This is the question: https://i.stack.imgur.com/iTOFw.png

However, in Divergence Theorem, a double integral over the surface is equal to a triple integral over a region. And in this question, there is only one integral over a surface. I have no idea how to do it.

Answer 1

Hint 1: $$ F={(xy^2, yz^2,zx^2) \over \sqrt{x^2+y^2+z^2}} $$

Hint 2: $$\sqrt{x^2+y^2+z^2}=?$$