Question

question
the circumference of a circle is 10π ft. what is the area, in square feet? express your answer in terms of π.
answer attempt 1 out of 2
a =
ft²
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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 \( C = 10\pi \) ft. So, \( 10\pi = 2\pi r \).

Step2: Solve for radius \( r \)

Divide both sides of \( 10\pi = 2\pi r \) by \( 2\pi \): \( r=\frac{10\pi}{2\pi}=5 \) ft.

Step3: Recall area formula

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

Step4: Substitute \( r = 5 \) into area formula

Substitute \( r = 5 \) into \( A=\pi r^{2} \), we get \( A=\pi(5)^{2}=25\pi \) square feet.

Answer:

\( 25\pi \)