Park City Mathematics Institute Secondary School Teacher Program

The Water-Flask Problem

A transparent flask in the shape of a right rectangular prism is partially filled with water. When the flask is placed on a table and tilted, with one edge of its base fixed, several geometric shapes of various sizes are formed by the flask's face and the surface of the water. The shapes and sizes may vary according to the degree of tilt or inclination.

Download Geometer's Sketchpad® file: water_flask.sketch.gsp

Try to discover as many invariant relations (rules) concerning these shapes and sizes as possible. Write down all your findings.

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With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.