Question

find the area of a circle with a circumference of 6.28 units.
□ units²
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Explanation:

Step1: Recall the circumference formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius. We know \( C = 6.28 \) and we can use \( \pi \approx 3.14 \). So we solve for \( r \):
\( 6.28 = 2\times3.14\times r \)

Step2: Solve for the radius \( r \)

Simplify the right - hand side: \( 2\times3.14 = 6.28 \), so the equation becomes \( 6.28=6.28r \). Divide both sides by \( 6.28 \): \( r=\frac{6.28}{6.28}=1 \) unit.

Step3: Recall the area formula

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Now that we know \( r = 1 \) and \( \pi\approx3.14 \), we substitute \( r \) into the formula.

Step4: Calculate the area

Substitute \( r = 1 \) into \( A=\pi r^{2} \): \( A = 3.14\times1^{2}=3.14\times1 = 3.14 \) square units.

Answer:

\( 3.14 \)