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Math Help - word problem, fuel tank

  1. #1
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    word problem, fuel tank

    A cylindrical fuel storage tank has a diameter of 13 ft. The fuel stored in the tank has a density of  0.80 g  cm^{-3} and is used in a furnace at a rate of 2.95 lbm per minute. If the depth of fuel in the tank is initially 18.7 ft, what is the depth of fuel in the tank after the furnace has been running for three days? Express your answer in meters.
    I think these are the only conversion factors needed, I dont have trouble doing the conversion of units, rather the question it self. Cant make sense of it, any help appreciated. How do I work out the depth, if I dont know the height of the cylinder.

    Thanks


    1 ft = 0.304m

    1000 g = 2.205 lbm
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Using the density, find the volume required per minute.

    From the volume required per minute, divide by the cross-sectional area of the cylinder to get the decrease in height per minute.

    This decrease occurs in 1 minutes.

    In 1 day, there are 24 hours, 24*60 minuntes.

    In 3 days, there are 24*60*3 minutes.

    Find the total change in height now, using the time and rate of decrease in time.
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  3. #3
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    Is the axis of the cylinder horizontal or vertical? If vertical then the "cross section area" unknown008 refers to is a constant- the area of a circle of radius 6.5 feet. If horizontal, then this is NOT a "Pre-Algebra and Algebra" problem!
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  4. #4
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    ^^ I dont know, but I dont think I am meant to be using calculus for this.
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  5. #5
    MHF Contributor Unknown008's Avatar
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    Well, I would guess it's vertical since the initial height of the fule is more than the diameter

    So, cross-sectional area remains constant.

    Or if it's slant... that's another story!
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  6. #6
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    Quote Originally Posted by Tweety View Post
    I think these are the only conversion factors needed, I dont have trouble doing the conversion of units, rather the question it self. Cant make sense of it, any help appreciated. How do I work out the depth, if I dont know the height of the cylinder.

    Thanks


    1 ft = 0.304m

    1000 g = 2.205 lbm
    The overall height of the cylinder is not relevant- only the height of the fuel oil in the tank. You are told that the tank has radius 6.5 feet and the fuel has height 18.7 feet. Calculate the volume of that.

    From the fuel usage information given, calculate the volume of fuel used, and subtract that from the original volume. That will give the volume of fuel remaining. Divide by the cross section area to get the height of that fuel.
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