If C=12π , what is the area of the circle? (1 point)

Question

Responses

12π
12 pi

144π
144 pi

24π
24 pi

36π

Answer 1

The circumference $C$ of a circle is given by the formula:

$$C=2\pi r$$

where $r$ is the radius. Given $C=12\pi$, we can set up the equation:

$$2\pi r=12\pi$$

Dividing both sides by $2\pi$ gives:

$$r=\frac{12\pi }{2\pi }=6$$

Now that we have the radius, we can calculate the area $A$ of the circle using the formula:

$$A=\pi r^2$$

Substituting $r=6$:

$$A=\pi (6^2)=\pi (36)=36\pi$$

Therefore, the area of the circle is $36\pi$.

The correct response is:

36π