To find the area of the circular mirror, follow these steps:
1. Determine the radius of the circle:
- Given that the diameter of the mirror is 12 inches, we can find the radius by dividing the diameter by 2. Therefore,
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{12}{2} = 6 \text{ inches}.
\][/tex]
2. Recall the formula for the area of a circle:
- The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi r^2,
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
3. Substitute the radius into the formula:
- Using the radius we calculated, which is 6 inches, we substitute [tex]\( r = 6 \)[/tex]:
[tex]\[
A = \pi (6)^2 = \pi \times 36 = 36\pi \text{ square inches}.
\][/tex]
So, the area of the mirror is:
[tex]\[
A = 36\pi \text{ square inches}.
\][/tex]
The correct answer is:
C. [tex]\( 36\pi \)[/tex]
