To determine the length of the radius of a circle given the circumference, we use the relationship between the circumference and the radius. The formula for the circumference ([tex]\(C\)[/tex]) of a circle is:
[tex]\[ C = 2 \pi r \][/tex]
where [tex]\(r\)[/tex] is the radius and [tex]\(\pi\)[/tex] is a constant approximately equal to 3.14159.
1. We're given the circumference [tex]\(C = 36 \pi\)[/tex] feet.
2. Substitute [tex]\(C\)[/tex] into the formula:
[tex]\[ 36 \pi = 2 \pi r \][/tex]
3. To solve for the radius [tex]\(r\)[/tex], divide both sides of the equation by [tex]\(2 \pi\)[/tex]:
[tex]\[ r = \frac{36 \pi}{2 \pi} \][/tex]
4. Simplify the fraction by canceling [tex]\(\pi\)[/tex] on both the numerator and the denominator:
[tex]\[ r = \frac{36}{2} \][/tex]
5. Calculate the resulting division:
[tex]\[ r = 18 \][/tex]
Therefore, the length of the radius of the circle is [tex]\(18\)[/tex] feet.
So the correct answer is:
[tex]\[ \boxed{18 \text{ ft}} \][/tex]
