Final answer:
The volume of a cylinder doubles when the radius is doubled. With the new radius, the volume of the cylinder is four times its original volume.
Step-by-step explanation:
The volume of a cylinder is calculated by the formula V=πr²h, where V is the volume, r is the radius of the base, and h is the height.
When the radius is doubled, the new radius will be 2r. Substituting 2r into the cylinder volume formula, we get V'=π(2r)²h=4πr²h.
This volume is four times the original volume of the cylinder with a radius r. So, if you double the radius of a cylinder, its volume will increase four times over the original volume.
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