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 2 out of 2
a =
ft²
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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 \( C = 10\pi \) ft. So, \( 10\pi = 2\pi r \). Dividing both sides by \( 2\pi \), we get \( r=\frac{10\pi}{2\pi}=5 \) ft.

Step2: Recall area formula

The formula for the area of a circle is \( A=\pi r^{2} \). Now that we know \( r = 5 \) ft, substitute \( r \) into the area formula: \( A=\pi(5)^{2}=\pi\times25 = 25\pi \) square feet.

Answer:

\( 25\pi \)