Question

the circumference of a circle is 119.32 miles. what is the circles area? c = 119.32 mi round your answer to the nearest hundredth. square miles

Explanation:

Step1: Recall circumference formula

The formula for the circumference of a circle is \( C = 2\pi r \), where \( C \) is the circumference and \( r \) is the radius. We know \( C = 119.32 \) miles, so we can solve for \( r \). Rearranging the formula gives \( r=\frac{C}{2\pi} \). Substituting \( C = 119.32 \) and using \( \pi\approx3.14 \), we get \( r=\frac{119.32}{2\times3.14}=\frac{119.32}{6.28} = 19 \) miles.

Step2: Recall area formula

The formula for the area of a circle is \( A=\pi r^{2} \). Now that we know \( r = 19 \) miles, we substitute \( r = 19 \) and \( \pi\approx3.14 \) into the formula. So \( A = 3.14\times19^{2}=3.14\times361 = 1133.54 \) square miles.

Answer:

1133.54