To find the radius of a circle given the circumference, we can use the relationship between the circumference and the radius.
1. Recall the formula for the circumference [tex]\( C \)[/tex] of a circle in terms of the radius [tex]\( r \)[/tex] and the mathematical constant [tex]\( \pi \)[/tex]:
[tex]\[ C = 2 \pi r \][/tex]
2. We are given the circumference [tex]\( C = 16 \pi \)[/tex] feet.
3. Substitute [tex]\( 16 \pi \)[/tex] for [tex]\( C \)[/tex] in the circumference formula:
[tex]\[ 16 \pi = 2 \pi r \][/tex]
4. To solve for [tex]\( r \)[/tex], divide both sides of the equation by [tex]\( 2 \pi \)[/tex]:
[tex]\[ r = \frac{16 \pi}{2 \pi} \][/tex]
5. Simplify the right-hand side of the equation:
[tex]\[ r = \frac{16}{2} \][/tex]
6. Calculate the division:
[tex]\[ r = 8 \][/tex]
Therefore, the radius of the circle is 8 feet.
