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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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When a cylindrical tank is filled with water at a rate
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Updated on: 02 Feb 2019, 07:42
Updated on: 02 Feb 2019, 07:42
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When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?
A. \(\frac{\sqrt{10}}{2}\)
B. \(\sqrt{10}\)
C. \(4\)
D. \(5\)
E. \(10\)
A. \(\frac{\sqrt{10}}{2}\)
B. \(\sqrt{10}\)
C. \(4\)
D. \(5\)
E. \(10\)
Originally posted by GreenlightTestPrep on 02 Feb 2019, 06:39.
Last edited by Carcass on 02 Feb 2019, 07:42, edited 1 time in total.
Last edited by Carcass on 02 Feb 2019, 07:42, edited 1 time in total.
Formatted the answer choices
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: When a cylindrical tank is filled with water at a rate
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04 Feb 2019, 08:31
04 Feb 2019, 08:31
2
GreenlightTestPrep wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?
A. \(\frac{\sqrt{10}}{2}\)
B. \(\sqrt{10}\)
C. \(4\)
D. \(5\)
E. \(10\)
A. \(\frac{\sqrt{10}}{2}\)
B. \(\sqrt{10}\)
C. \(4\)
D. \(5\)
E. \(10\)
Let's examine what occurs in a 1-hour period
The volume of water increases by 22 cubic meters.
The height of the water increases by 0.7 meters.
So, we need to find the radius of a 0.7 meter high cylinder that has a volume of 22 cubic meters.
Volume = (pi)(radius²)(height)
22 = (pi)(radius²)(0.7)
IMPORTANT: notice that (pi)(0.7) = approximately 2.2
So, we get: 22 ≈ (2.2)(radius²)
Divide both sides by 2.2: 10 ≈ radius²
Solve: radius ≈ √10
Answer: B
Cheers,
Brent
Re: When a cylindrical tank is filled with water at a rate
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07 Oct 2023, 13:28
07 Oct 2023, 13:28
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