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The Volume Of A Layer Of Lead Of Uniform Thickness(word problem)

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    A container in the form of a rectangular prism measuring 2m by 3m by 4m is covered with a layer of lead shielding of uniform thickness. Model the volume of the shielding as a function of its thickness. Treat the shelding as a hollow rectangular prism. DO NOT SIMPLIFY.



    2. Relevant equations
    V=lxwxh


    3. The attempt at a solution

    I found

    l = 4m w = 3m h = 2m

    when i drew each shape as a 2d shape. I noticed that the layer of lead was an equal (Uniform) layer around. So i labeled one unit of thickness, as t.

    Thus all sides ended up having a layer on either side...

    i came to conclude that the new measurements were.

    L2=4 + 2t W2= 3 + 2t H2 = 2 + 2t

    and since its hollow..

    V(t) = L2*W2*H2 - Lwh

    V(t) = (4+2t)(3+2t)(2+2t) - 4*3*2 <====(Or 24)




    Can anyone tell me if this solution appears to be correct, and also point me out if i'm forgetting where any layers thickness maybe ?
     
  2. jcsd
  3. Mar 12, 2012 #2

    Dick

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    Looks fine to me.
     
  4. Mar 12, 2012 #3
    I think your answer looks good. I think you chose what your variable represented nicely and set up your function good. You can always check yourself in these situations to see if your answer makes sense. Does your equation make sense? In this case, the volume of the thickness should approach 0 as t approaches zero, and it does; so your equation seems reasonable.

    Only "qualm" I would have is that you "found" l, h, and w. It would be better to let l, h, and w be the values they are, unless they specifically gave you equations for finding them. Just a little nitpick, I'm sure your teacher won't mind but it just makes it a little more rigorous.

    But, again, for word problems there is usually a way to check and see if your solution makes sense. Let something get really small or really big and see if the answer makes sense, in this case it does!
     
  5. Mar 12, 2012 #4


    Thanks a lot guys i really appreciate it.

    and so in terms of what you're saying with the approaching business.

    i would know my answer shouldn't be correct if it was a negative number, cause volume can't be negative?

    or like, can you explain to me a little more in depthly abuot the approaching bussiness and the equation.?
     
  6. Mar 12, 2012 #5

    Dick

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    I'm not sure there's really much you need to check. It's a straighforward problem and you did it in a straightforward way. I really wouldn't worry about it.
     
  7. Mar 12, 2012 #6
    Yea you`re right no need to complicate things. I Really appreciate that you checked my answer and for your input man. It means a lot to me man keep up the great help man.
     
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