All the arc's cross the radius on hole numbers, 3rd one is 4 from the edge, 2nd is 9 from the edge 1st is 16 from the edge.

The radius of the circle is 11

The radius of each arc's circle is 16.

find area of section's 1, 2, 3, and 4. I know this could be placed into a geometry section, but it looks easier to solve using calculus - areas between 2 arc's on X-Y axis, then double.

I know were to start, find the points where each arc intercepts the edge of the circle, using for the 3rd arc:

$\displaystyle (x-23)^2 - y^2 = 16^2$

$\displaystyle -x^2 - y^2 = 11^2$

- that makes more sense when placed on an axis - the center of the circle creating the 3rd arch is 23 units away from the center of the circle.

(line them up subtract, solve for x then solve for y)

.. im sure its pretty simple once given the correct fourmla..