Question

the circumference of a circle is 12π m. what is the area, in square meters? express your answer in terms of π.

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. Given $C=12\pi$, we have $2\pi r=12\pi$.

Step2: Solve for the radius

Divide both sides of the equation $2\pi r = 12\pi$ by $2\pi$. So, $r=\frac{12\pi}{2\pi}=6$ m.

Step3: Recall area formula

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

Step4: Calculate the area

Substitute $r = 6$ into the area formula: $A=\pi\times6^{2}=36\pi$ $m^{2}$.

Answer:

$36\pi$