Class 5 Boiler Practice Exam

How many times does doubling the size of a pipe increase its capacity?

1. Two times

2. Three times

3. Four times

4. Five times

The correct answer is: Four times

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.