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Harry Houdini was a famous escape artist. In this project we relive a trick of his that challenged his mathematical prowess, as well as his skill and bravery. It will challenge these qualities in you as well!
Houdini had his feet shackled to the top of a concrete block which was placed on the bottom of a giant laboratory flask. The cross-sectional radius of the flask, measured in feet, was given as a function of height y from the ground by the formula
with the bottom of the flask at y=1 foot.
The flask was then filled with water at a steady rate of 22 cubic feet per minute. Houdini's job was to escape the shackled before he was drowned by the rising water in the flask.
Now Houdini knew it would take him exactly 10 minutes to escape the shackles. For dramatic impact, he wanted to time his escape so it was completed precisely at the moment the water level reached the top of his head. Houdini was exactly six feet tall.
Your task is to find out how high this block should be. Express the volume of the water in the flask as a function of the
height of the liquid above ground level. What is the volume when the water level reaches the top of Houdini’s head? (Neglect
Houdini’s volume and the volume of the block.) What is the height of the block?
Left Hand Rule
Right Hand Rule
Mid Point Rule