The International Baccalaureate
Mathematical Exploration
Topic:
Figures of infinite area or volume
Personal Code: hlt648
Session: May 2020
Declaration:
I declare that this work is my own work and is the final version. I have acknowledged each use of the
words or ideas of another person, whether written, oral or visual.
1
, Table of Contents
Rationale.................................................................................................................................................. 3
Introduction............................................................................................................................................. 3
Main body................................................................................................................................................ 4
Solids of revolution.............................................................................................................................. 4
Gabriel's Horn ...................................................................................................................................... 5
Drinking Vessel .................................................................................................................................... 9
General proof for solids of revolution of finite surface area and infinite volume ............................ 10
Real life reflection ............................................................................................................................. 13
Conclusion and reflections ................................................................................................................ 14
Bibliography........................................................................................................................................... 15
2
Mathematical Exploration
Topic:
Figures of infinite area or volume
Personal Code: hlt648
Session: May 2020
Declaration:
I declare that this work is my own work and is the final version. I have acknowledged each use of the
words or ideas of another person, whether written, oral or visual.
1
, Table of Contents
Rationale.................................................................................................................................................. 3
Introduction............................................................................................................................................. 3
Main body................................................................................................................................................ 4
Solids of revolution.............................................................................................................................. 4
Gabriel's Horn ...................................................................................................................................... 5
Drinking Vessel .................................................................................................................................... 9
General proof for solids of revolution of finite surface area and infinite volume ............................ 10
Real life reflection ............................................................................................................................. 13
Conclusion and reflections ................................................................................................................ 14
Bibliography........................................................................................................................................... 15
2
