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Homework Help: Urgent: Help with Estimating Total Area

  1. Jan 24, 2010 #1
    This is not a HW but someone said in a previous thread that it sounds like it so I will post it here because it fits the format I guess.

    1. The problem statement, all variables and given/known data

    I have a flat plat that is x by y. It has an unknown number of holes in it but I do know the diameter of the holes is D.

    I also know that s/D = 4 where s is the spacing between holes of diameter D. Using this how can I estimate the total area absent in the flat plat, i.e. the amount missing.

    2. Relevant equations

    s/D = 4

    area rectangle = x*y

    area circle = pi*r^2

    D = 0.05"

    x = 4

    y = 3

    3. The attempt at a solution

    I've been over thinking this but I can maybe estimate the amount of circles of diameter D can possible fit in there and leave it at that but is there a mathematical way to do this as oppose to me just drawing it out and guessing the amount of holes.
  2. jcsd
  3. Jan 24, 2010 #2
    find s find the total area of x and y d=.05" d/2 = radius of the wholes and find the area of one and divide the area of x and y by the area of the holes and find the equation this is basic math with a twist to it why did u need help?
  4. Jan 24, 2010 #3
    I don't see where you used s.

    Also, I do not know how many holes there are so I can't just find the equation. If I knew the amount of holes and therefore cannot calculate the area of holes.

    The area of holes is what I am trying to estimate. I'm thinking I have to use the expression s/D = 4.

    It might be something simple but I miss simple things. Sorry if it offends you.
  5. Jan 24, 2010 #4
    Hi higha level

    Yes, you have to use the expression s/D = 4 to find s. Actually, you can determine the number of holes that contained in the plat.

    Let's consider the x-side. Basically, you have x, D, and s. Just think a simple one. If D = 1, then s = 4, so if x = 3, you can only have 1 circle on x-side. Now do it regarding the data from the question. :smile:
  6. Jan 25, 2010 #5
    That's what I was saying I did.

    D = 0.05" so I got a s= 0.2".

    x = 4 inch so therefore there probably can only be about 15 circles along x. And subsequently 11 in the y=3. This gives an estimate of 165 circles and I can calculate the missing area, etc. I previously did this already and moved forward. The question wasn't a hw problem but someone said it sounded like it.

    My question was is there a simple way to calculated it with an equation using s/D to find that missing area without finding the amount of holes there are? Still coming up with a relatively close answer?

    Sorry if I didn't ask correctly before.
  7. Jan 25, 2010 #6
    I don't think there's a way to find the missing area without finding the number of circles...
  8. Jan 25, 2010 #7


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    Homework Helper

    Just for clarification, is s the distance between the outsides of the circles or the centres of the circles?
    Also, I am assuming here that the circles are formed in a pattern such that the first and second rows are in a straight line parallel to each other, except the circles in the second row are not vertically beneath the circles in the first row. As such:

    http://img687.imageshack.us/img687/3927/circleareaapprox.png [Broken]

    I was surprised to find that the diameter of each circle isn't needed to find the answer, all you need is x and y.

    I'll give the answer now, and if you're interested in the maths behind it, just ask. And I haven't tested the result myself so be weary. Use at own risk :wink:

    The area, A, of all the circles combined by using the layout I showed above is given by [tex]A\approx \frac{\pi}{25\sqrt{3}}xy[/tex]
    The constant would be more appropriately approximated: therefore [tex]A\approx 0.073 xy[/tex]

    If you can post a picture of what the layout of the design is, we could give a better approximation.
    Last edited by a moderator: May 4, 2017
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