Question

find the area of a circle with a circumference of 50.24 units.

Explanation:

Step1: Recall circumference formula

The formula for the circumference of a circle is \( C = 2\pi r \), where \( C \) is the circumference and \( r \) is the radius. We know \( C = 50.24 \) units. Let's solve for \( r \).
\( 50.24 = 2\pi r \)
Assuming \( \pi \approx 3.14 \), we can rewrite the equation as:
\( 50.24 = 2\times3.14\times r \)
\( 50.24 = 6.28r \)

Step2: Solve for radius \( r \)

Divide both sides of the equation by \( 6.28 \) to find \( r \):
\( r=\frac{50.24}{6.28} = 8 \) units.

Step3: Recall area formula

The formula for the area of a circle is \( A=\pi r^{2} \). Now that we know \( r = 8 \) units and \( \pi\approx3.14 \), we can substitute \( r \) into the formula.

Step4: Calculate the area

\( A = 3.14\times8^{2} \)
First, calculate \( 8^{2}=64 \). Then, multiply by \( 3.14 \):
\( A = 3.14\times64 = 200.96 \)

Answer:

\( 200.96 \)