Question

the water department for a city is deciding on which pipe configuration to use to deliver water to its residents. it can choose to use one pipe with a radius of 8 centimeters, or a set of two pipes, each with a radius of 4 centimeters. 1. which pipe configuration can deliver more water to the residents, one 8 - cm pipe or two 4 - cm pipes? show your work and explain your reasoning.

Explanation:

Step1: Calculate area of 8 - cm pipe

The cross - sectional area of a circle is $A=\pi r^{2}$. For a pipe with $r = 8$ cm, $A_1=\pi\times(8)^{2}=64\pi$ $cm^{2}$.

Step2: Calculate area of two 4 - cm pipes

For each pipe with $r = 4$ cm, the area of one pipe is $A_{single}=\pi\times(4)^{2}=16\pi$ $cm^{2}$. The total area of two such pipes is $A_2 = 2\times16\pi=32\pi$ $cm^{2}$.

Step3: Compare the areas

Since $64\pi>32\pi$, the one 8 - cm pipe has a larger cross - sectional area.

Answer:

The one 8 - cm pipe can deliver more water to the residents because its cross - sectional area ($64\pi$ $cm^{2}$) is larger than the combined cross - sectional area of two 4 - cm pipes ($32\pi$ $cm^{2}$).