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Rate Filling Tank = Radius

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bml1105 Really wants to Beat The GMAT!
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Rate Filling Tank = Radius Post Mon May 19, 2014 9:38 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    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) (√10)/2
    (B) √10
    (C) 4
    (D) 5
    (E) 10


    Correct Answer: B

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    Post Mon May 19, 2014 9:50 am
    bml1105 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) (√10)/2
    (B) √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)r²h
    22 = (pi)r²(0.7)

    IMPORTANT: notice that (pi)(0.7) = approximately 2.2

    So, we get: 22 = (2.2)r²
    Divide both sides by 2.2: 10 = r²
    Solve: r = √10 (approximately)

    Answer: D

    Cheers,
    Brent

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    Post Mon May 19, 2014 10:37 am
    Hi bml1105,

    This question can also be solved by TESTing THE ANSWERS.

    Volume of a cylinder is…

    V = (pi)(R^2)H

    With a given height of .7 meters, we can TEST the answers to find the one that gives us a Volume of 22.

    While I would normally start with B or D, I'm going to start with C (since it's the smallest of the "nice" answers and it's right in the "middle" of the options)

    If R = 4, we'd have….

    (pi)(4^2)(.7) = 16pi(.7) = approximately 35

    This result is TOO BIG (it's supposed to be 22). This means we can eliminate C and anything bigger than C (D and E).

    Let's test B next. If R = √10…..

    (pi)(10)(.7) = 7pi = approximately 22. This is a MATCH for what we were told.

    Final Answer: B

    GMAT assassins aren't born, they're made,
    Rich

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