Final answer:
To find the circumference of a circle with an area of 64π ft², first solve for the radius using the area formula. Then apply the circumference formula to get the answer, which is 16π feet.
Step-by-step explanation:
The question involves finding the circumference of a circle whose area is given as 64π ft². The first step is to identify the formula for the area of a circle, which is A = πr². With the given area, we can solve for the radius r. Here are the steps:
- Set the area formula equal to 64π: πr² = 64π.
- Divide both sides by π to solve for r²: r² = 64.
- Take the square root of both sides to find r: r = 8 ft.
- Now, use the formula for circumference, which is C = 2πr, substituting 8 ft for r.
- Therefore, C = 2π(8 ft) = 16π ft.
Thus, the circumference of the circle is 16π feet.