IB Math SL IA

Calculating the volume of the Coca Cola bottle using simultaneous equations and integration

1. Introduction

This investigation aims to calculate the volume of the Coca-Cola bottle. My inspiration for this investigation arose after studying the depths of geometry and calculus. I was intrigued by the method of measuring the volume of an irregular geometric shape using solid of revolution. In looking around for an area of research, I tried to apply what I learnt in my classes to an object used in day to day life. I have seen many objects with varied geometric shapes but I was interested by the unique contour shape of the Coca-Cola bottle. Unlike other simple straight-sided bottles, the Coca-Cola bottle had a body with an outward curving centre and a narrow lid. Since the patent of its design in 1915, Coca- Cola has successfully created a strong image for its brand by offering bottles with iconic curved fluted lines. The unique bottle shape inspired me to investigate how to calculate its volume.

The topic is of significance because measurement had heavy implications on scientific field. Measurement is the process of assigning a numeric value to properties of an object by making a comparison with a standard.1 Historically, measurement provided scientists with a base to investigate the world around them and form theories. For instance, measurement systems were used primarily for measuring the area of land, predicting river flooding, and construction of buildings, thus contributing to the development of geometry and astronomy.2 Therefore, investigation on the method of measuring the volume of unfamiliar shapes is important in a variety of fields, including science and industry…