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25 Mar 2021, 22:00
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Intake Pipe: $3,000
Outlet Pipe: $6,000
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:30) correct
34%
(02:26)
wrong
based on 717
sessions
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A hydroelectric plant is refurbishing its intake and outlet pipes, both of which are cylindrical and open on both ends. The intake pipe has a length of 20 meters and a diameter of 10 meters, while the outlet pipe has a length of 50 meters and a diameter of 8 meters. The refurbishment process involves refinishing the entire outer surface area of each pipe at a cost of $5 per square meter.
In the table below, select the approximate cost to refurbish the intake pipe and the outlet pipe, assuming that the wall of the pipe has negligible thickness.
In the table below, select the approximate cost to refurbish the intake pipe and the outlet pipe, assuming that the wall of the pipe has negligible thickness.
| Intake Pipe | Outlet Pipe | |
| $3,000 | ||
| $6,000 | ||
| $12,000 | ||
| $15,000 | ||
| $18,000 |
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Official Answer
Intake Pipe: $3,000
Outlet Pipe: $6,000
25 Mar 2021, 22:28
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Official Explanation
The trick here is that, when finding the surface area of the pipe, we don’t have to find the area of the circle on the top or the bottom of the cylinder. Since the pipe is open, we only need to find the surface area of the rectangular portion that makes up the surface of the pipe: \(2πrh.\) For the intake pipe, the radius is 5 and the length is 20, so its surface area is \(2 * π * 5 * 20\), which gives a surface area of \(200π\) square meters. Since our values are fairly spread out, we can estimate \(π\) as 3 to give us a total surface area of 600 square meters. At $5 per square meter, the total cost will be \(600 * 5 = $3,000\). For the outlet pipe, the surface area is \(2 * π * 4 * 50\), or \(400π. 400 * 3\) gives us a surface area of roughly 1200 square meters, so the cost will be \(1200 * 5 = $6,000.\)
Intake Pipe: $3,000
Outlet Pipe: $6,000
The trick here is that, when finding the surface area of the pipe, we don’t have to find the area of the circle on the top or the bottom of the cylinder. Since the pipe is open, we only need to find the surface area of the rectangular portion that makes up the surface of the pipe: \(2πrh.\) For the intake pipe, the radius is 5 and the length is 20, so its surface area is \(2 * π * 5 * 20\), which gives a surface area of \(200π\) square meters. Since our values are fairly spread out, we can estimate \(π\) as 3 to give us a total surface area of 600 square meters. At $5 per square meter, the total cost will be \(600 * 5 = $3,000\). For the outlet pipe, the surface area is \(2 * π * 4 * 50\), or \(400π. 400 * 3\) gives us a surface area of roughly 1200 square meters, so the cost will be \(1200 * 5 = $6,000.\)
Intake Pipe: $3,000
Outlet Pipe: $6,000
General Discussion
25 Mar 2021, 22:12
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Not sure what I did wrong here.
The SA of the a cylinder excluding the top/bottom faces is 2πr^2h
Intake: 2πr^2h = 2π(5)^2 x 20 = 40 x 25π = 1000π --> 1000π x 5 = 5000π = ~ 15000
Outake: 2πr^2h = 2π(4)^2 x 50 = 100 x 16π = 1600π --> 1600π x 5 = 8000π = ~24000
Sajjad1994 do you have the answer?
The SA of the a cylinder excluding the top/bottom faces is 2πr^2h
Intake: 2πr^2h = 2π(5)^2 x 20 = 40 x 25π = 1000π --> 1000π x 5 = 5000π = ~ 15000
Outake: 2πr^2h = 2π(4)^2 x 50 = 100 x 16π = 1600π --> 1600π x 5 = 8000π = ~24000
Sajjad1994 do you have the answer?
