Linear stochastic programming/easy formulas

I have a question about some stochastic linear programming formulas, namely (4.3),(4.4),(4.5) and (4,6) in the snippet below. I do not follow how was created the argument of $$c$$ in (4.3), the formula (4.4) and from (4.4) the formula (4.5), and finally (4.6). I'm looking on it almost a week without any success.

The snippet is taken from the book Introduction to stochastic programming by John Birge,the second edition.

• Thank you for your interest. My problem is how $\frac{w\cdot \pi \cdot x^2}{4}$ was created. And also both sides of the inequality $\frac{w}{\xi^3}\leq 39.27$ was created. And finally $\frac{w^3}{\xi^4}\leq 63,169$ and $Q(w,x,\xi)$. Just as I've said in my OQ, all the (,)'s. Are they all just ilustration examples with no rule ? Is $c$ a variable or rather a function in (4.3) ? – user3357120 Sep 25 '19 at 18:32