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Re: Volume of an oblique frustum of a right cone.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121210] Re: Volume of an oblique frustum of a right cone.
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sun, 4 Sep 2011 04:13:52 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <3738989.73229.1315049476998.JavaMail.root@m06>

For a cone of heigh H, radius R, and tipping angle from the vertical of
angle, I calculate the volume as:

(H \[Pi] R^2 (H Cos[angle] - R Sin[angle])^3)/(3 (H^2 Cos[angle]^2 - 
   R^2 Sin[angle]^2)^(3/2))

I have a notebook (using Presentations) giving a step by step derivation
with dynamic displays that I will send to anyone who sends a request to me.


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  




From: Matthias Bode [mailto:lvsaba at hotmail.com] 

Hola:

I completely fail to find a function that decribes the emptying of a right 
cone as a function of its inclination.

To illustrate the problem:
We have a right cone (e. g. a common cocktail glass completely filled with 
liquid) with a base angle alpha. When we incline the cone from its upright 
position to ninety degrees minus alpha/2 - then it will be empty - what is 
volume of the remaining liquid inside the cone as a function of the cone's 
inclination from its originally vertical position?
(It's not homework; I'm retired and trying to teach my daughter, 10th g
rade German grammar school, the use of MATHEMATICA.)

Best regards,

MATTHIAS BODE
S 17.35775=B0, W 066.14577=B0
2'740 m
AMSL.





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