To find the radius of the cylinder, we can use the formula for the volume of a cylinder, which is given by:

Volume = π * r^2 * h

where:

• Volume is the volume of the cylinder,
• π is the mathematical constant pi (approximately 3.14159),
• r is the radius of the cylinder, and
• h is the height of the cylinder.

We are given that the height of the cylinder is four times the radius, which can be expressed as h = 4r.

We are also given that the volume of the cylinder is 256 cm³. Plugging these values into the volume formula:

256 = π * r^2 * (4r)

Now, we can solve for r:

256 = 4πr^3

Divide both sides by 4π:

r^3 = 64

Now, take the cube root of both sides to find r:

r = ∛64

r = 4

So, the radius of the cylinder is 4 cm.