Question

the circumference of a circle is 87.92 kilometers. what is the circles area?
c = 87.92 km
round your answer to the nearest hundredth.
square kilometers

Explanation:

Step1: Find the radius from circumference

The formula for the circumference of a circle is \( C = 2\pi r \). We can solve for \( r \) by rearranging the formula: \( r=\frac{C}{2\pi} \). Given \( C = 87.92 \) km, we substitute the value into the formula. So \( r=\frac{87.92}{2\times3.14} \) (using \( \pi\approx3.14 \)). First, calculate \( 2\times3.14 = 6.28 \), then \( r=\frac{87.92}{6.28}=14 \) km.

Step2: Calculate the area of the circle

The formula for the area of a circle is \( A=\pi r^{2} \). We know \( r = 14 \) km and \( \pi\approx3.14 \), so substitute \( r \) into the formula: \( A = 3.14\times14^{2} \). First, calculate \( 14^{2}=196 \), then \( A = 3.14\times196 = 615.44 \) square kilometers.

Answer:

615.44