# Pool Math

**Calculus**Level 4

Having nothing better to do, you place a rigid iron bar inside a section **c** of an empty pool such that either end of it lies on the same plane and touch the insides of the pool. You then choose a point **P** on the bar such that the distance to one end is **7** and the distance to the other end is **3**, with the length of the bar being **10**. Finally, you move the bar in a way that, at any given time, neither end leaves **c**.

Suppose that each pool is a surface such that its horizontal sections are convex closed curves.

After one lap - at the moment the bar is back where it was first placed - what is the area between the curve covered by point **P** and the border of **c**, rounded to the closest integer?