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When a cylindrical tank is filled with water at a rate

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When a cylindrical tank is filled with water at a rate [#permalink] New post 02 Feb 2019, 06:39
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Question Stats:

75% (02:20) correct 25% (03:23) wrong based on 4 sessions
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. \(10\)
[Reveal] Spoiler: OA

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Last edited by Carcass on 02 Feb 2019, 07:42, edited 1 time in total.
Formatted the answer choices
1 KUDOS received
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Re: When a cylindrical tank is filled with water at a rate [#permalink] New post 04 Feb 2019, 08:31
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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. \(10\)


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
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Re: When a cylindrical tank is filled with water at a rate   [#permalink] 04 Feb 2019, 08:31
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When a cylindrical tank is filled with water at a rate

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