If you double the size of a pipe, how many times does its capacity increase?

When you double the size of a pipe, it's essential to understand how volume is affected by changes in dimensions. The capacity of a pipe is related to its cross-sectional area and the length of the pipe. For circular pipes, which is a common shape in piping systems, the area is determined by the formula (A = \pi r^2), where (r) is the radius.

If you double the diameter of the pipe, the radius also doubles. Consequently, when the radius is doubled, the new area becomes (A_{new} = \pi (2r)^2 = \pi (4r^2) = 4A_{original}). This means that the cross-sectional area increases fourfold.

Since the length of the pipe remains the same, the capacity of the pipe, which is essentially the volume that can flow through it, increases by the same factor as the area. Therefore, when the diameter is doubled, the overall capacity of the pipe increases four times. This is why the correct answer is that the capacity increases fourfold when the diameter is doubled.