here is my take... I'm getting x = 10 as an answer. Here was my approach.
Overall: the area of the large circle minus the area of the small circle will give the area of the shaded region.. the following is how this looks mathematically:
Recall: Area of a circle is defined by πr² and I will be using 'x' as the radius of the smaller circle. So:
324π is the area of the large circle and (x)²(π) represents the area of the smaller circle:
Now 324π - x²(π) = 224π
or, 324 - x² = 224
or x² = 100
and now you can see x = 10
