The figure below shows three small circles, each with a diameter of 6 centimeters, inside a larger circle.
image
What is the area of the shaded part of the figure?
A.
72
π
square centimeters
B.
81
π
square centimeters
C.
54
π
square centimeters
D.
216
π
square centimeters
B. 81π square centimeters
To find the shaded area, first find the area of each small circle and subtract it from the area of the large circle. The area of each small circle is π(3)^2 = 9π square centimeters. Since there are 3 small circles, the total area of the small circles is 3 * 9π = 27π square centimeters.
The diameter of the large circle is equal to the sum of the diameters of the 3 small circles, making it 3 * 6 = 18 centimeters. The radius of the large circle is therefore 9 centimeters.
Therefore, the area of the large circle is π(9)^2 = 81π square centimeters.
Finally, the area of the shaded part is 81π - 27π = 54π square centimeters.
So, the answer is C. 54π square centimeters.