Cutting a Wedge out of a Disk to Make a Cone

Date: 12/05/2005 at 00:28:42
From: Dave
Subject: I need formula for angles & degrees of a cone.

I am building a hopper cone 69' in circumference and with a 37 degree
slope.  The diameter will be approximately 22' at the top and the
height will be approximately 8'.  I need to know how large of a wedge
(in degrees) to cut out of a circle in order to make this cone.  Is
there a formula for this?  Also, if I were to change the slope of the
cone, how would this affect the degrees of the needed wedge?

Date: 12/05/2005 at 09:47:14
From: Doctor Jerry
Subject: Re: I need formula for angles & degrees of a cone.

Hello Dave,

Thanks for writing to Dr. Math.  So that we use the same terminology,
please take a look at 

     

The "finished" cone is on the left.  The flat piece of metal from
which the cone is cut is on the right.  The edge VB on the right
becomes edge VB on the left.  The angles t and T are measured in
radians.  Once you have an answer in radians, you can convert it to
degrees by multiplying the radian measure times 180/pi.

Given any two of h, r, and t, the third can be found using the formula

  tan(t) = r/h.

The values of R and T are given by

  R = sqrt(h^2 + r^2)

  T = (2*pi*r)/R .

Please write back with any questions.  I'd regret it if you were to
cut a large piece of metal and it came out badly.

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/