GROUP MEMBERS:

CONTENT PAGE

|No. |Content |Page(s) | |1. |Introduction | | |2. |Definition | | |3. |History | | |4. |Part I | | |5. |Part II | | |6. |Part III | | |7. |Further Exploration | | |8. |Reflection | |

INTRODUCTION

We students taking Additional Mathematics are required to carry out a project work while we are in Form Five. This year the Curriculum Development Division Ministry of Education has prepared four tasks for us. We are to choose and complete only ONE task based on our area of interest. This project can be done in groups or individually, but each of us are expected to submit an individually written report.

I think the additional mathematics project work is a very good opportunity for us to test and enhance our thinking skills. We are given 6 weeks time frame to complete the assignment and I believe I have the luxury of time to think, think and think over the solutions to those questions. And the point of all of this is to learn new things and explore new horizons in mathematical fields.

On this project I am working on, I hope to be able to make generalization about the volume and the weight of a cake for the occasion of Teachers Day celebration. Through the use of various mathematical methods like calculus, trial-and-improve method and graph, I am certainly and fairly to be able to achhieve my goal. I would like to point out that by using correct and suitable mathematical method and calculation, I sincerely wish that my project will be able to be implemented and achieve the desired results.

Definition

Pi, π has the value of 3.14159265. In Euclidean plane geometry, π is defined as the ratio of a circle's circumference to its diameter.

[pic] π=[pic]

The ratio [pic] is constant, regardless of a circle's size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, C, preserving the ratio [pic].

Alternatively π can also be defined as the ratio of a circle's area (A) to the area of a square whose side is equal to the radius.

[pic] π=[pic]

A BRIEF HISTORY AND FACTS ABOUT CAKES

Cake is a form of food, typically a sweet, baked dessert. Cakes normally contain a combination of flour, sugar, eggs, and butter or oil, with some varieties also requiring liquid (typically milk or water) and leavening agents (such as yeast or baking powder). Flavorful ingredients like fruit purées, nuts or extracts are often added, and numerous substitutions for the primary ingredients are possible. Cakes are often filled with fruit preserves or dessert sauces (like pastry cream), iced with buttercream or other icings, and decorated with marzipan, piped borders or candied fruit. Cake is often the dessert of choice for meals at ceremonial occasions, particularly weddings, anniversaries, and birthdays. There are countless cake recipes; some are bread-like, some rich and...

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