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Help with net for a frustum

  1. Nov 13, 2014 #1
    I need to make a net for a frustum. The following web page explains how to do it... http://www.analyzemath.com/Geometry/conical_frustum.html

    I have tried but am unable to do this complicated, advanced (o.k basic) math.

    In the following figure I have the values R,r and h.
    conical_frustum_1.gif

    R = 40
    r = 35
    h = 83

    I need the values for x,y,t and H in the following figure so I can construct my net.
    conical_frustum_2.gif

    x = ?
    y = ?
    t = ?
    H = ?

    Can anyone please help me find x,y,t,H ???
     
    Last edited: Nov 13, 2014
  2. jcsd
  3. Nov 13, 2014 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Your internet must not be working properly. If you read on the linked article further, it gives explicit formulas to calculate x, y, and t.

    H can be calculated knowing the Pythagorean Theorem:

    H2 = h2 + (R-r)2

    From the article:

    x = r H / (R - r)
    y = r H / (R - r) + H

    Any of the formulas 2 Pi r = x t or 2 Pi R = y t may be used to find the central angle t (in radians):

    t = 2 Pi r / x

    = 2 Pi r / [ r H / (R - r) ]

    = 2 Pi (R - r) / H

    Since the angle t is in radians, to convert t to degrees

    t in degrees = t in radians * 180 / Pi

    Remember, measure twice, cut once.
     
  4. Nov 13, 2014 #3
    No I'm just terrible at this stuff. I did read the solutions given on that page and went through their working example but I still don't understand it.

    Here is what I do to solve the Pythagorean Theorem:

    H² = h² + (R-r)²

    H² = 83x83 + 5x5

    H² = 6889 + 25

    H² = 6914

    H = 1 (6914 / 6914)

    I divided the last number by itself as H² is H times by itself. :/
    Clearly that's not right but i don't properly understand how to solve the equation or where i'm going wrong.
    I think once I have got H i can do the next bit as it seems a bit easier.

    I am all for learning how to do this but find it difficult. I appreciate the much needed help.


    And in my case calculate ten times before asking on PF.
     
  5. Nov 13, 2014 #4
    O.k I went ahead and cheated and used an online calculator to solve the Pythagorean problem.
    So..

    H= 83.15046602394962

    I then did this..

    x = r H / (R - r)
    x = 35 x 83.15 / (40-35)
    x = 2910.25 / 5
    x = 582.05

    y = r H / (R - r) + H
    y = 35 x 83.15 / (40 - 35) + 83.15
    y = 2910.25 / 5 + 83.15
    y = 665.2

    t = 2 Pi r / x
    t = 2 x 3.141 x 35 / 582.05
    t = 219.87 / 582.05
    t = 0.38

    t in degrees = 0.38 x 180 / Pi
    t in degrees = 21.78


    So my final values are

    H = 83.15
    x = 582.05
    y = 665.2
    t = 21.78°

    Is that correct?
     
  6. Nov 13, 2014 #5

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Your numbers look pretty good. Remember, for H, x, and, y to use consistent measurement units like inches or centimeters when laying out your net.

    When you have something like

    H2 = 6914

    the square root is what tells you how to find H, that is, what number when multiplied by itself, gives you 6914 in this case.

    Your calculator has a key that looks like a little check mark √ which is what you press after entering 6914.
     
  7. Nov 13, 2014 #6
    Ah yes that makes sense^
    Thanks very much for the help. The page I linked to confused me saying 'sqrt ' before the equations. I get it now. Much appreciated.
     
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