Add Maths Sba

Ruel Wallace Add Maths S.B.A Mr. Teesdale 5-8

Table of Contents
Cover page……………………………………………………………………………………………1
Table of contents…………………………………………………………………………………..2
Title……………………………………………………………………………………………………...3
Problem Statement………………………………………………………………………………..4
Mathematical Formulation…………………………………………………………………….5
Problem Solution…………………………………………………………………………………..7
Application of Solution…………………………………………………………………………14
Conclusion…………………………………………………………………………………………...15

Title
A mathematical investigation of an experimental package design by Trini Chocolate Designs Ltd. with the goal of minimizing volume of content of packaging and manufacturing cost using Calculus, Trigonometry and Pythagoras Theorem.

Problem Statement
To determine how effective a container is, in adequately storing chocolate and how innovative the use of the package will be. Trigonometry Pythagoras Theorem and Calculus is used to determine:
1) The max cross sectional area of the pentagonal prism
2) The minimum value of the contents
3) Amount material needed for packaging
4) The minimum number of containers in order to make a profit

Mathematical Formulation
In part, (a) we insert a perpendicular bisector at A dropping at the midpoint, M; of EB, which results in two right angle triangles. The base of one triangle must be half of the base, DC, which is 8xcm thus making MB 4xcm. Tan ABE is given as 3/4c. Using tanθ = opposite ÷ adjacent A

E B

D