Question

the circumference of a circle is 55.264 miles. what is the circles area?
c = 55.264 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 need to solve for \( r \). Given \( C = 55.264 \) miles, we can rearrange the formula to \( r=\frac{C}{2\pi} \).
Substituting the value of \( C \), we get \( r = \frac{55.264}{2\times3.14} \) (using \( \pi\approx3.14 \)).
First, calculate the denominator: \( 2\times3.14 = 6.28 \).
Then, \( r=\frac{55.264}{6.28}=8.8 \) miles.

Step2: Recall area formula

The formula for the area of a circle is \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. We now know \( r = 8.8 \) miles, so substitute \( r \) into the formula.
\( A = 3.14\times(8.8)^{2} \).
First, calculate \( (8.8)^{2}=77.44 \).
Then, \( A = 3.14\times77.44 = 243.1616 \).

Step3: Round to nearest hundredth

Rounding \( 243.1616 \) to the nearest hundredth (two decimal places), we look at the third decimal place, which is 1. Since 1 < 5, we don't round up the second decimal place. So, \( A\approx243.16 \) square miles.

Answer:

243.16