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Explain Bot To find the shaded region between two overlapping circles, you need to find the area of each circle and subtract the overlapping area.
First, calculate the area of each circle using the formula:
Area = πr^2
For the circle with a radius of 9:
Area1 = π(9)^2
For the circle with a radius of 4:
Area2 = π(4)^2
Next, calculate the overlapping area. This can be done by finding the area of the intersection of the two circles.
To find the overlapping area, you can use the formula for the area of a circular segment:
Overlapping Area = r^2 × arccos((d^2 + r^2 - R^2) / (2dr)) - (1/2) × (√((-d + r + R)(d + r - R)(d - r + R)(d + r + R))), where r is the radius of one circle, R is the radius of the other circle, and d is the distance between the centers of the two circles.
In this case, the overlapping area will be calculated using the above formula with r = 9, R = 4, and d = 9 + 4 = 13.
Now, you can plug in the values and calculate the overlapping area.
Overlapping Area = (9^2) × arccos((13^2 + 9^2 - 4^2) / (2 × 13 × 9)) - (1/2) × (√((-13 + 9 + 4)(13 + 9 - 4)(13 - 9 + 4)(13 + 9 + 4)))
Finally, subtract the overlapping area from the sum of the individual circle areas to get the shaded region:
Shaded Region = Area1 + Area2 - Overlapping Area
Now, you can substitute the values you calculated and solve for the shaded region.