To find the area of the circle, let's follow these steps:
1. Calculate the radius from the circumference: The formula for the circumference of a circle is given by:
[tex]\[
C = 2 \pi r
\][/tex]
Where [tex]\( C \)[/tex] is the circumference and [tex]\( r \)[/tex] is the radius. We are given the circumference [tex]\( C = 167 \)[/tex] cm.
Solving for the radius [tex]\( r \)[/tex]:
[tex]\[
r = \frac{C}{2 \pi} = \frac{167}{2 \pi} \][/tex]
Using the given numerical result:
[tex]\[
r \approx 26.58 \, \text{cm}
\][/tex]
2. Calculate the area using the radius: The formula for the area [tex]\( A \)[/tex] of a circle is given by:
[tex]\[
A = \pi r^2
\][/tex]
Substitute the radius:
[tex]\[
A \approx \pi (26.58)^2
\][/tex]
3. Compute the area:
[tex]\[
A \approx \pi \times 706.44
\][/tex]
Where [tex]\( 706.44 \)[/tex] comes from [tex]\( (26.58)^2 \)[/tex]. Therefore, the area calculation in terms of [tex]\( \pi \)[/tex] is:
[tex]\[
A \approx 706.44\pi \, \text{square centimeters}
\][/tex]
Given the answer choices:
A) [tex]\( 16\pi \)[/tex]
B) [tex]\( 32\pi \)[/tex]
C) [tex]\( 64\pi \)[/tex]
D) [tex]\( 256\pi \)[/tex]
The numerical area we computed in terms of [tex]\(\pi\)[/tex] is [tex]\( 706.44 \pi \)[/tex]. This value does not match any of the provided options directly. Thus, none of the options (A, B, C, or D) correctly represent the actual area of the circle based on the given data.
