Question

problem 5c
a circular field has a circumference of 240π feet.
what is the area of the field?
square feet
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Explanation:

Step1: Recall circumference formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius. We know \( C = 240\pi \), so we set up the equation \( 2\pi r = 240\pi \).

Step2: Solve for radius \( r \)

Divide both sides of \( 2\pi r = 240\pi \) by \( 2\pi \). So \( r=\frac{240\pi}{2\pi}=120 \).

Step3: Recall area formula

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \).

Step4: Calculate the area

Substitute \( r = 120 \) into the area formula: \( A=\pi(120)^{2}=\pi\times14400 = 14400\pi \).

Answer:

\( 14400\pi \)