Pipeline

By what percentage does the cross-sectional area of a pipe decrease if the circular cross-section is replaced by a square with the same perimeter?

Final Answer:

p =  21.46 %

Step-by-step explanation:

$$\begin{gathered} p=100\frac{S_1-S_2}{S_1} \\ p=100(1-\frac{S_2}{S_1}) \\ p=100(1-\frac{a^2}{\pi r^2}) \\ p=100(1-\frac{a^2}{\pi r^2}) \\ o=2\pi r=4a \\ \pi r=2a \\ p=100(1-\frac{a^2}{\pi (2a/\pi {)}^2}) \\ p=100(1-\frac{1}{\pi 4/{\pi }^2}) \\ p=100\cdot (1-\frac{\pi }{4})=100\cdot (1-\frac{3.1416}{4})=21.46\% \end{gathered}$$

Try another example