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Math Help - Weight of pipe

  1. #1
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    Question Weight of pipe

    Can someone please help me with the following problem?

    An iron pipe is 21 m long & its exterior diameter is 8 cm. If the thickness of the pipe is 1 cm & iron weight 8 g/cu.cm, find the weight of the pipe.

    How do I do this? I have found the volume of the pipe by first finding the external volume, then the internal volume & then finding the difference but what do I do after that to find the weight?

    Thanks,

    Ron
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  2. #2
    A Plied Mathematician
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    Just multiply by the given density of iron. Note that you're asked to find the weight, not the mass. Thus, you'll need also to multiply by g.
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  3. #3
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    I tried what you suggested but am not getting the correct answer. This is what I did:

    External Volume=22*4*4*2100/7=105600 cu.cm
    Internal Volume=22*3*3*2100/7=59400 cu.cm
    Volume=105600-59400=46200 cu.cm

    Weight (or mass...whatever it is)=46200*8=369600 gm=369.6 kg

    But the answer is 92.4 kg.

    Thanks,

    Ron
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  4. #4
    A Plied Mathematician
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    I get essentially what you get. I think the figure of 92.4 kg is incorrect.
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  5. #5
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    e^(i*pi)'s Avatar
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    Assuming it's a cylinder then, as for all prisms the volume is cross sectional area multiplied by length or V = \pi r^2 h = \dfrac{\pi}{4}d^2h. You may also have a unit mismatch - your length is in metres but the diameter is cm!

    V_1 = \dfrac{\pi}{4} \cdot 8^2 \cdot 2100 = 33600\pi \text{ cm}^3 -- this is the whole cylinder

    Edited this lineBy the same token: V_2 = 18900\pi \text{ cm}^3 (you should see if you can figure out where this figure came from) -- this is the volume of empty air on the insde

    Edited this lineHence the difference in volumes \Delta V = V_1 - V_2 = 33600\pi - 18900\pi = 14700\pi \text{ cm}^3 -- this is the volume taken up by the tube itself

    m = \rho V = 8 \cdot 10^{-3} \cdot 14700\pi = 117.6\pi \approx 369.45 \text{kg , (3sf)}


    The weight (your question erroneously uses kg to describe weight so they might mean find the mass) is given by W = mg = 117.6g \pi \text{ N}

    I don't get your answer but I can't see where I went wrong.

    Edited - thanks to Ackbeet pointing out where I went wrong
    Last edited by e^(i*pi); February 5th 2011 at 08:32 AM. Reason: removing a dodgy pi
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  6. #6
    A Plied Mathematician
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    e^(i pi):

    The thickness of the pipe is 1 cm. You used 7 as the inner diameter, but the thickness has to be subtracted twice from the outer diameter in order to get the inner diameter.
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