Question

the circumference of a circle is 12.56 feet. what is the circles area?
c = 12.56 ft
round your answer to the nearest hundredth.
square feet

Explanation:

Step1: Recall the formula for circumference of a circle.

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius. We know \( C = 12.56 \) feet and we can use \( \pi \approx 3.14 \). So we can solve for \( r \):
\( 12.56 = 2\times3.14\times r \)

Step2: Solve for the radius \( r \).

First, simplify the right - hand side: \( 2\times3.14 = 6.28 \), so the equation becomes \( 12.56 = 6.28r \). Then, divide both sides by 6.28: \( r=\frac{12.56}{6.28}=2 \) feet.

Step3: Recall the formula for the area of a circle.

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). We know \( r = 2 \) feet and \( \pi\approx3.14 \).

Step4: Calculate the area.

Substitute \( r = 2 \) into the area formula: \( A = 3.14\times2^{2} \). First, calculate \( 2^{2}=4 \), then \( 3.14\times4 = 12.56 \) square feet.

Answer:

\( 12.56 \)