Final answer:
The area of the circular mirror with a circumference of 30π is 225π square units.
Step-by-step explanation:
The circumference of the circular mirror is given as 30π. We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. So, if we have C = 30π, we can solve for the radius by dividing both sides of the equation by 2π: r = 30π / 2π = 15.
Once we have the radius, we can calculate the area of the mirror using the formula A = πr². Plugging in the value of the radius we found, A = π(15)² = 225π square units.