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Conical Section

  • Thread starter zorro
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  • #1
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Homework Statement



Suppose there is a Conical section (of a right circular cone) of total height 'l' and radii 'a' and 'b' (a>b). How do we derive the formula for the radius at a height 'h' (h<l) ?


Homework Equations





The Attempt at a Solution

 
Last edited:

Answers and Replies

  • #2
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Draw a cross section through the middle and look for similar triangles whose properties you can use to solve your problem. (I think you are describing a frustrated cone, not a pure cone?)
 
  • #3
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I am talking about this (see attached file).
 

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  • #4
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Draw a cross section through the middle and look for similar triangles whose properties you can use to solve your problem. (I think you are describing a frustrated cone, not a pure cone?)
Good advice, but the term is "frustum of a cone."
 
  • #5
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Good advice, but the term is "frustum of a cone."
Haha :rofl: (or in other words, a truncated cone)
How was his advice good? We can't use similar triangle property to find the radius.
 
  • #6
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Extend the vertical line at the center and the outer sloped line up until they meet, then you'll have similar triangles.
 
  • #7
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Forget the 3 dimensional aspect; it would be easier to think of a trapezoid with one side of length [itex]l[/tex], perpendicular to sides a & b. Call the remaining side c.

a & b still represent the upper and lower radii of your truncated cone, and r represents the radius of that object at height h above side a.
 

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  • #8
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Extend the vertical line at the center and the outer sloped line up until they meet, then you'll have similar triangles.
I find the algebra easier if you construct the additional 2 line segments shown in the attached drawing.
 

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  • #9
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Thanks alot zgozvrm. I got my answer :smile:
 
  • #10
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Glad to help.

What did you come up with?
 
  • #11
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r = a - h(a-b)/l
 
  • #12
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Very nice!
 

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