To find the area of the shaded region, we need to calculate the area of the larger circle and the two smaller circles and then subtract them from each other.
1. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
2. To find the area of the larger circle, we use the radius labeled as 9 centimeters:
A1 = π(9)^2
3. To find the area of the smaller circle, we use the radius labeled as 4 centimeters:
A2 = π(4)^2
4. Since the two smaller circles touch each other and the larger circle, the total area of the two smaller circles is:
A3 = 2 * A2
5. Finally, to find the shaded region area, we subtract the sum of the areas of the two smaller circles from the area of the larger circle:
Shaded Area = A1 - A3
Now, let's calculate:
A1 = π(9)^2 = 81π
A2 = π(4)^2 = 16π
A3 = 2 * A2 = 2 * 16π = 32π
Shaded Area = 81π - 32π = 49π
The area of the shaded region is 49π square centimeters.
Unfortunately, none of the given answer choices match the calculated area. Please double-check the question or provide additional information to calculate the correct answer.