"The" angle on a circle is always the "minor arc".

Yes, the radius of the larger circle is 3 times the radius of the smaller circle. It follows that the area of the larger circle is 9 times the area of the smaller circle. But that is NOT the area of the shaded region. The shaded region is the larger circle minus the smaller circle. So if we call the area of the smaller circle "A", the area of the larger circle is 9A. That means that the area of the shaded region is 9A- A= 8A.