[최종 18/20 7점] Math AA HL Internal Assessment

주제: Minimising the surface area of packaging using calculus

RQ: Do global companies make use of environmentally optimal packaging?

AA HL syllabus에서 배우는 미적분과 대학수준의 multivariable calculus를 잘 설명하고, 환경보존 이라는 global issue까지 잘 포함시켜 M23세션에서 18/20라는 높은 점수를 받을 수 있었습니다.

[본문내용]

Introduction
While participating in numerous beach cleanups throughout high school, I frequently encountered plastic bottles and paper packaging littering the shores. This prompted me to
investigate the harm caused by packaging to the environment, and I was shocked to discover that in 2018 alone, packaging products produced a staggering 82.2 million tons of waste,
significantly contributing to the global waste problem. Waste damages the environment in a variety of ways. For example, disposing of waste often requires burning it, which releases
carbon dioxide and air pollutants. Alternatively, simply dumping trash in landfills releases large amounts of methane, another greenhouse gas. As a student aspiring to be a chemical engineer who can make a positive impact on the environment through green chemistry, I saw this Math IA as a great opportunity to play a role in reducing environmental damage.

Aim and rationale
In this exploration, I will address the issue of wasteful packaging. Through my study of optimisation using calculus, I discovered how it can be applied to minimise the amount of material used in packaging. Hence, the specific aim of this investigation will be finding the minimum surface area for a fixed volume V of common shapes used in packaging, such as
cuboids(eg. cardboard boxes) and cylinders(eg. soft drinks cans), and also the dimensions that allow us to obtain that minimum surface area, using optimisation by calculus. Minimising the surface area of packaging whilst keeping its volume constant will significantly reduce the materials needed to produce it while allowing it to contain the same amount of goods- this will decrease the amount of waste generated by the packaging when it is thrown away. Hence, this investigation will hopefully contribute to mitigating the global waste problem by creating a guideline for optimal packaging that firms can follow…

• 총 페이지수: 24 pages
• 주제: Minimising the surface area of packaging using calculus
• 과목명: Mathematics
• The file is in PDF format.