### Instruction: What is the area, in square units, of a circle with a circumference of $8\pi$ units? Express your answer in terms of $\pi$.### Response: To find the area of a circle, I need to know its radius.
The circumference of a circle is related to the radius by the formula $C = 2\pi r$, where $C$ is the circumference and $r$ is the radius.
I can use this formula to solve for the radius, given the circumference of $8\pi$ units.
Dividing both sides of the equation by $2\pi$, I get $r = \frac{C}{2\pi} = \frac{8\pi}{2\pi} = 4$ units.
Now that I have the radius, I can use the formula for the area of a circle, which is $A = \pi r^2$, where $A$ is the area and $r$ is the radius.
Plugging in the value of $r = 4$, I get $A = \pi (4)^2 = 16\pi$ square units.
This is the final answer.