What occurs when a 1" pipe is changed to a 2" pipe regarding the cross-sectional area?

When changing a pipe from a 1" diameter to a 2" diameter, the cross-sectional area increases significantly due to the nature of the area calculation for a circle. The cross-sectional area ( A ) of a circular pipe is determined using the formula ( A = \pi \left( \frac{d}{2} \right)^2 ), where ( d ) is the diameter of the pipe.

For a 1" pipe, the radius is ( \frac{1}{2} = 0.5 ) inches. Thus, the area ( A_1 ) would be calculated as:

[ A_1 = \pi \left(0.5\right)^2 = \pi \left(0.25\right) = 0.785 \text{ square inches.} ]

For a 2" pipe, the radius is ( \frac{2}{2} = 1 ) inch. Therefore, the area ( A_2 ) is:

[ A_2 = \pi \left(1\right)^2 = \pi \left(1\right) = 3.14 \text{ square inches.} ]

To find the increase