String of Beads Puzzle

This is a nifty problem from Presh Talwalkar.

“This is from a Manga called Q.E.D. I thank Sparky from the Philippines for the suggestion!

A string of beads is formed from 25 circles of the same size. The string passes through the center of each circle. The area enclosed by the string inside each circle is shaded in blue, and the remaining areas of the circles are shaded in orange. What is the value of the orange area minus the blue area? Calculate the area in terms of r, the radius of each circle.”

See the String of Beads Puzzle