How does the volume of a cylinder change when its diameter is quadrupled?

If the radius of a cylinder is x, and the height is y, then the volume of the cylinder will be x²yπ. If every thing is quadrupled then it will be 4x and 4y, Therefore it will become (4x)²4yπ. This simplifies to 16x²4yπ, and then even further to 64x²yπ. Excluding the 64, that is the same as the original equation, so we now know that the coefficient of volume increase is 64, so the volume is 64 times greater. By the way, if you know the scale factor of change, the volume change will always be the scale factor change cubed. For area, or surface area it will be the scale factor squared. I hope this helps.