Final answer:
The circumference of a circle with an area of 64π in² is found by first determining the radius from the area formula and then applying the circumference formula to find that the circumference is 16π inches.
Step-by-step explanation:
The question asks us to find the circumference of a circle given that its area is 64π in². To find the circumference, we first need to determine the radius of the circle using the formula for the area of a circle, A = πr². We know that A = 64π, so we can set up the equation 64π = πr². Dividing both sides by π, we get r² = 64, and by taking the square root, we find that r = 8 inches.
Once we have the radius, we can use the circumference formula C = 2πr to find the circumference. Substituting 8 inches for r, we get C = 2π(8) = 16π inches. Therefore, the circumference of the circle is 16π inches.
It's important to understand that when working with pi (π), precision matters, and it can be approximated as 3.14159. However, for most schoolwork problems, using π in your calculations is acceptable unless specified otherwise.