Doubling the radius of this cylindrical barrel would quadruple the volume.
Step-by-step explanation:
The volume of a cylinder of radius and height is:
.
If radius stays the same, volume would be proportional to height . That is, . Doubling height would only double .
If height stays the same, volume would be proportional to , the square of the radius. That is, . Doubling radius would quadruple and thus quadruple as required.