Final answer:
The problem pertains to finding the height of a cylinder when its volume and radius are known. Using the volume formula of a cylinder we can substitute and solve for h, concluding that the height of the cylinder is 4 cm.
Step-by-step explanation:
The question is asking for the height of a cylinder given the volume and the radius. We start solving this problem using the formula for the volume of a cylinder that is V = πr²h, where V is the volume, r is the radius and h is the height. We have been given that the volume, V, is 64π cubic centimeters and radius, r, is 4 cm. Therefore, we can substitute these values into the volume equation as follows: 64π = π(4²)h. Simplify on the right side of the equation to get: 64π = 16πh.
Next, dividing both sides of the equation by 16π to isolate h (the height), you'd get: h = 64π/16π. Simplifying, we conclude that the height, h, of the cylinder is 4 cm.
Learn more about Cylinder Volume