you are a construction worker who is laying down concrete drainage pipes. each pipe is 5 feet long and 3…

you are a construction worker who is laying down concrete drainage pipes. each pipe is 5 feet long and 3 inches thick, and has an outside diameter of 6.5 feet. you lay down 4 drainage pipes end to end. at any given time, what is the volume of water that passes through the 4 drainage pipes at half capacity? round the answer to the nearest tenth of a cubic foot. 141.3 165.8 282.6 306.6 565.2

you are a construction worker who is laying down concrete drainage pipes. each pipe is 5 feet long and 3 inches thick, and has an outside diameter of 6.5 feet. you lay down 4 drainage pipes end to end. at any given time, what is the volume of water that passes through the 4 drainage pipes at half capacity? round the answer to the nearest tenth of a cubic foot. 141.3 165.8 282.6 306.6 565.2

Answer

Explanation:

Step1: Convert pipe thickness to feet

3 inches = 3/12 = 0.25 feet.

Step2: Calculate inner - diameter of the pipe

Outer diameter = 6.5 feet, so inner diameter $d=6.5 - 2\times0.25=6$ feet, and radius $r = \frac{d}{2}=3$ feet.

Step3: Calculate cross - sectional area of one pipe at half - capacity

The cross - sectional area of a semi - circle is $A=\frac{1}{2}\pi r^{2}$, where $r = 3$ feet. So $A=\frac{1}{2}\pi\times3^{2}=\frac{9\pi}{2}$ square feet.

Step4: Calculate volume of water in one pipe

Length of each pipe $l = 5$ feet. Volume of water in one pipe $V_1=A\times l=\frac{9\pi}{2}\times5=\frac{45\pi}{2}$ cubic feet.

Step5: Calculate volume of water in 4 pipes

Volume of water in 4 pipes $V = 4\times V_1=4\times\frac{45\pi}{2}=90\pi\approx282.7$ cubic feet, rounded to the nearest tenth is 282.6 cubic feet.

Answer:

282.6