# Circular Hole Drilled in a Cone

Initializing live version

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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

## 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

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send