Question

question
the circumference of a circle is 6π cm. what is the area, in square centimeters? express your answer in terms of π.
answer
attempt 2 out of 2
a =
cm²
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Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius of the circle. We are given that \( C = 6\pi \) cm. So we set up the equation \( 2\pi r = 6\pi \).

Step2: Solve for the radius \( r \)

Divide both sides of the equation \( 2\pi r = 6\pi \) by \( 2\pi \).

$$ r=\frac{6\pi}{2\pi}=3 $$

So the radius of the circle is 3 cm.

Step3: Recall the formula for the area of a circle

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

Step4: Substitute the value of \( r \) into the area formula

We know that \( r = 3 \), so substitute \( r = 3 \) into the formula \( A=\pi r^{2} \).

$$ A=\pi\times(3)^{2}=9\pi $$

Answer:

\( 9\pi \)