Final answer:
A 12 inch pipe can carry four times the volume of water than a 6 inch pipe if both have the same flow rate and velocity, because the area of a pipe, which determines its carrying capacity, increases with the square of the radius.
Step-by-step explanation:
Assuming the same flow rate and velocity, a 12 inch pipe carries four times the volume of water that a 6 inch pipe does. This is determined by the area of a circle, which is πr², where r is the radius. Since the 12 inch pipe has a radius twice that of the 6 inch pipe, its area, and therefore the volume of water it can carry at any given time, is four times greater.