To find the area of a circle given its diameter, you can use the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
Step-by-step:
1. Find the radius of the circle:
The diameter of the circle is 16 feet. The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[ r = \frac{diameter}{2} = \frac{16}{2} = 8 \, \text{feet} \][/tex]
2. Substitute the radius into the area formula:
[tex]\[ A = \pi r^2 \][/tex]
[tex]\[ A = \pi (8)^2 \][/tex]
3. Calculate the expression:
[tex]\[ A = \pi \cdot 64 \][/tex]
Therefore, the expression that gives the area of the circle in square feet is:
[tex]\[ A = 64 \cdot \pi \][/tex]
Reviewing the given options:
A. [tex]\( 8 \cdot \pi \)[/tex] is not correct.
B. [tex]\( 16 \cdot \pi \)[/tex] is not correct.
C. [tex]\( 8^2 \cdot \pi \)[/tex] simplifies to [tex]\( 64 \cdot \pi \)[/tex], which is correct.
D. [tex]\( 16^2 \cdot \pi \)[/tex] is not correct.
The correct choice is:
C. [tex]\( 8^2 \cdot \pi \)[/tex]
