Question

the circumference of a circle is 25.12 yards. what is the circles area? round your answer to the nearest hundredth. square yards

Explanation:

Step1: Find the radius of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=25.12\) yards and \(\pi\approx3.14\), we can solve for \(r\):
\(25.12 = 2\times3.14\times r\)
\(25.12 = 6.28r\)
\(r=\frac{25.12}{6.28}=4\) yards.

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = 4\) and \(\pi\approx3.14\):
\(A=3.14\times4^{2}\)
\(A=3.14\times16\)
\(A = 50.24\) square yards.

Answer:

\(50.24\)