Minor arc $AB$ in the diagram is $30^\circ$ and the radius of the circle is $6.$ Find the area of circular segment $AB.$ [asy] size(6cm);

The area of the sector is 6^2*30/180*pi = 6*pi, and the area of the triangle is 6^2*sin(30) = 18, so the area of the circular segment is 6*pi - 18.