 # Circular Hole Drilled in a Cone

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This Demonstration lets you explore the shape of the difference between a cone and a circular cylinder.

Contributed by: Erik Mahieu (February 2014)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Consider a cylinder of radius , with axis at a distance from the axis and at a height above the - plane. Its parametric equations are , , ,

where and are parameters.

The parametric equations of a right cone with base radius and height are , , ,

where and are parameters.

The intersection curve of the two surfaces can be obtained by solving the system of three equations for three of the four parameters . In this Demonstration, solving for , , and gives the parametric equations for the intersection curve with parameter (the curve consists of two parts, depending on the sign inside the equation for ): , , ,

with and .

## Permanent Citation

Erik Mahieu

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