# 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