10178

# A Perfect Cognac Glass

The traditional measure of cognac is to place the glass on its side and fill to the brim. An equally popular measure is to place the glass vertically and fill to point of maximum surface area. For a given glass curvature and stem length, by adjusting the base width we can create the perfect cognac glass, where the two measures are equal. Varying the stem length will adjust the base so that the measure is not changed.

### DETAILS

The cognac glass is described by its radial function , where is the height when the glass is sitting on its base. In order to calculate the traditional measure of cognac (when the glass is placed on its side), we need the area enclosed by the chord created by the cognac level . That area is simply the area of its sector minus the area of its isosceles triangle. The volume is then equal to the integral over from 0 to (the brim of the glass), and depending on , we must switch between the upper and lower areas enclosed by the chord. The popular measure of cognac (when the glass is placed standing up) is simply , where is the point of maximum surface area.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.