In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. the area of the shaded region is 288π cm2. what is the value of x?

The area of the shaded part is given by:
Area=(area of the outer circle)-(area of the inner circle)
A=πr²
Area of outer circle:
Area=π(2x)²=4πx²

area of inner circle
area=π×6²=36π
thus the area of the shaded part will be:
4πx²-36π=288π
π(36-4x²)=288π
-36+4x²=288
4x²=324
x²=81
x=9