For $b > 0$, the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{b^{2}} = 1$ encloses the same area as the circle $x^{2} + y^{2} = 20$. What is $b$?

Explanation

1. 01

   The circle has radius $\sqrt{20}$, so it encloses $20\pi$; the ellipse has $a = 5$ and encloses $5\pi b$.

2. 02

   $5\pi b = 20\pi$ gives $b = 4$.