The density of oil in a circular oil slick on the surface of the ocean at a distance of $r$ meters from the center of the slick is given by $\displaystyle \delta(r) = \frac{25}{1+r^2}$ kilograms per square meter. Find the exact value of the mass of the oil slick if the slick extends from $r = 0$ to $r = 10$ meters.

Mass = Include units in your answer.