To solve for the area of a circle with a given diameter of 16 feet, we need to follow these steps:
1. Determine the radius of the circle:
The radius is half of the diameter.
Since the diameter is 16 feet, the radius [tex]\( r \)[/tex] is:
[tex]\[
r = \frac{16}{2} = 8 \text{ feet}
\][/tex]
2. Use 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]
Substituting the value of the radius [tex]\( r = 8 \)[/tex] feet, we get:
[tex]\[
A = \pi (8)^2
\][/tex]
3. Simplify the expression:
Calculating [tex]\( 8^2 \)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
Thus, the area is:
[tex]\[
A = 64 \pi \, \text{square feet}
\][/tex]
4. Match this result with the given options to find the correct expression for the area:
- Option A: [tex]\( 8^2 \cdot \pi \)[/tex]
- Option B: [tex]\( 16 \cdot \pi \)[/tex]
- Option C: [tex]\( 16^2 \cdot \pi \)[/tex]
- Option D: [tex]\( 8 \cdot \pi \)[/tex]
We see that Option A matches our expression [tex]\( 8^2 \cdot \pi \)[/tex], which simplifies to [tex]\( 64 \pi \)[/tex].
Therefore, the expression that gives the area of the circle is:
[tex]\[
\boxed{8^2 \cdot \pi}
\][/tex]
