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Doubling the size of a pipe significantly increases its cross-sectional area, which directly affects its capacity. The capacity of a pipe is related to the area of the circle formed by its diameter. The area \(A\) of a circle is calculated using the formula \(A = \pi r^2\), where \(r\) is the radius of the circle.

When you double the diameter of a pipe, the new radius becomes twice the original radius. Therefore, the new area can be expressed as:

\[

A_{\text{new}} = \pi (2r)^2 = \pi (4r^2) = 4 \pi r^2

\]

This means that the new area is four times the original area. Since the capacity of the pipe is proportional to its cross-sectional area, doubling the size of the pipe increases its capacity by a factor of four. This is why the correct answer is that doubling the size of the pipe increases its capacity four times.