What is the area of the shaded region of a circle if the diameter is 18 centimeters and the area shaded is 270 degrees?

To find the area of the shaded region of the circle, first calculate the area of the entire circle using the formula ( A = \pi r^2 ). The radius ( r ) is half the diameter, so ( r = 9 ) cm. Thus, the area of the circle is ( A = \pi (9^2) = 81\pi ) square centimeters. Since the shaded region is 270 degrees, which is ( \frac{3}{4} ) of the circle, the area of the shaded region is ( \frac{3}{4} \times 81\pi = 60.75\pi ) square centimeters, approximately 191.1 square centimeters.