Question

A circular mirror has a diameter of 12 inches.

Part A
What is the area, in square inches, of the mirror?
A. 6pi
B. 12pi
C. 36pi
D. 72pi

Part B
A circular frame that is 3 inches wide surrounds the mirror.
What is the combined area, in square inches, of the circular mirror and the frame?
A. 9pi
B. 18pi
C, 54pi
D. 81pi

Answer 1

Part A

C. 36π

Part B

D. 81π

Explanation:

The general formula for the area of a circle is:

A = πr², where 'r' represents the radius of the circle

Since the mirror has a diameter of 12 inches, the radius is half of that measure, or 6 inches. So, for the area of just the mirror:

A = π6² = 36π in²

Adding a circular frame around the mirror increases the radius by another 3 inches:

6 in + 3 in = 9 in

Given the new radius, use the same formula to calculate the overall area:

A = π9² = 81π in²