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.