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
3647 cm.
what is the value of x?

Subtract the area of the inner circle (2pi*6^2) which is approximately 226.08 cm^2. So add this to the area of the shaded region to get 3873.08 cm^2. Substitute 2x in for r, the resulting equation is 3873.08 cm^2 = 2*pi*(2x)^2 or 8*pi*x^2. Divide both sides by 8pi. Results in 154.18 = x^2, so x is approximately 12.3-12.4.