Final answer:
To find the difference in the radii of two concentric circles with equal shaded and unshaded areas, set up the equation π(6^2 - r^2) = πr^2. Solving for 'r', we find the inner circle's radius to be 3√2. The difference in the radii is 6 - 3√2.
Step-by-step explanation:
To find the difference in the radii of the two concentric circles, we need to understand that the shaded area is equal to the unshaded area. Let's denote the radius of the inner circle as 'r'.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Since the shaded area is equal to the unshaded area, we can set up the equation: π(6^2 - r^2) = πr^2
Simplifying this equation, we get: 36 - r^2 = r^2
Combining like terms and isolating 'r', we find: 2r^2 = 36
Taking the square root of both sides, we get: r = √(36/2) = √18 = 3√2
Therefore, the difference in the radii of the two circles is 6 - 3√2.