If the radius of a cylinder is doubled, what happens to the volume?

To understand why the volume increases by four times when the radius of a cylinder is doubled, we can start with the formula for the volume of a cylinder, which is given by:

[ V = \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height of the cylinder.

When the radius is doubled, we can denote the new radius as ( 2r ). Plugging this new radius into the volume formula, we have:

[ V_{\text{new}} = \pi (2r)^2 h ]

This simplifies to:

[ V_{\text{new}} = \pi (4r^2) h ]

[ V_{\text{new}} = 4(\pi r^2 h) ]

This shows that the new volume is four times the original volume ( V ). Therefore, when the radius of a cylinder is doubled, the volume does indeed increase by four times, as indicated by the choice selected.

Understanding this geometric relationship illustrates how changes in linear dimensions affect the volume, as volume is influenced by the square of the radius due to its dependence on area (the base of the cylinder) and