A circle has an area of 64π square units. What is the diameter of the circle?

The area of a circle relates to its radius by A = πr2. Since the diameter is twice the radius, an area-to-diameter question always reduces to first solving for the radius from the given area, then relating it to the diameter.

1. Given: Area A = 64π square units. Using A = πr2, substitute: πr2 = 64π.

2. Divide both sides by π: r2 = 64.

3. Take the positive square root: r = 8 units.

4. Using the standard radius-diameter relationship, the diameter D = 16 units.

Cross-check: substituting r = 8 back into A = πr2 gives π(8)2 = 64π, which matches the given area — confirming the diameter is 16 units.