Designing a recycling bin for school that people will actually use, then modelling every component with geometry.
Math 10March 2026Completed with a classmate
The Problem
How many students a day choose to throw paper in the bins due to recycling being perceived as inconvenient and useless? Taking into account AES’s considerable amount of paper use, especially during exam season, we need to create a safe and supportive space for students and staff members to be able to recycle paper without being oblivious to the location of the recycling bin, along with the moral and ethical concept of recycling paper once used. According to Business Waste, a UK-based waste service organisation, a study conducted by the organisation found that educational institutions and systems in India consume roughly 3.8 million metric tons of paper every year, equivalent to 94.3 million trees. Another part of this study was evaluating that primary schools generate 45kg of waste per student, whereas secondary schools produce 22kg of waste individually. Moreover, 80% of the material is recyclable, though only 20% is actually recycled. (Business Waste; ‘School Waste’) After reviewing these immense statistics and knowing that a large part of this waste stems from schools like ours, we must collectively take action to reduce as much paper waste as possible.
The Design
Initially, when brainstorming for this project, we [my partner and I] considered a variety of shape ideas, ranging from a box-shaped bin with a divider and an opening latch at the bottom for removing the papers. Though we quickly modified our approach when we realised that the bin must be easily accessible for janitors and recycling support teams to remove the papers before they fill up. Moreover, a cuboid-shaped bin would likely have had sharp edges, making operations difficult for young students. This is when we considered creating a cylindrical bin to eliminate sharp edges and accommodate a larger amount of paper; a cylinder maximises internal volume while minimising the material required for the external surface. A cylindrical shape has curved sides, which also makes it easier to move the recycling bin around (reducing potential collisions by eliminating sides, leading to smoother interactions when passing the bin).
The geometric and tangible design of the paper bin holds significant importance in order to encourage students and faculty to actually use the bin. This includes the bin needing to be accessible, user-friendly, and prominent enough to grab attention. We decided to include multifunctional components in the bin in order to balance all these important aspects.
Front view (not to scale). Paper slides down the two inclined lids into separate compartments for single-sided and double-sided paper.
Components
Each part was modelled as a solid (cylinder, triangular prism, cuboid) to find its volume and surface area, then costed from material density and Indian market prices.
Component
Geometry
Material
Est. cost
Body
Hollow cylinder, 80 cm tall, outer radius 20 cm, inner radius 15 cm
Recycled HDPE plastic
₹2,550
Inclined lids ×2
Triangular prisms, 17 cm base, 20 cm deep, 16.39° slope
Recycled acrylic (PMMA)
₹557
Wheels ×4
Cylinders, radius 7.5 cm, 4 cm wide
Polypropylene casters with rubber tread
₹1,400
Lock latches ×4
8 × 6 × 2 cm prism with a curved hook
Stainless steel with rubber grip
₹872
Divider
75 cm tall, 30 cm wide, 0.5 cm thick
Aluminium sheet
₹13–17
Labels ×2
15 × 4 cm
Laminated PVC vinyl
₹10 each
Reflection
When I was working on this project, I felt it gave me so much insight and expanded my knowledge, as it incorporated math in a real-life problem, a solution, research, and in writing an essay, something I don’t think I had ever done before. To me, math is a language that, once you understand the base formula of it, you can easily understand and adapt to everything else that follows it. Though I had never thought to apply math to real life, working on this project was precisely that. Throughout this project, I developed a sense of seeing math in just about everything, something that my sister always claims she feels (‘once you start liking maths, you see it everywhere’). However, this was a thoroughly new type of project, which is likely what made it challenging and a bit exhausting, as it required new skills and new thought processes of overcoming issues and finding mathematical solutions while blending everything into an essay, which, moreover, needed logical and sound reasoning. I’ve created a multitude of different projects similar to this one, though I had not once thought about the mathematical aspect of it. Though energy-depleting, this project was genuinely so eye-opening, as it compelled me to see everything in great detail and precision, see the maths within everything. I believe that maths has a very introspective feel to it already, as it’s the study of numerical values and finding substantial solutions to a problem, demanding that people be more cognitively aware of their surroundings. When looking at service and creating something to aid our community, I believe that employing maths is a great way to do so, as it allows you to find the exact meticulous values and find logical solutions to real-world problems, taking everything into account, rather than simply making vague assumptions or guesses, which moreover increases the chances of creating something succesfull, as you’ve considered a number of solutions along with a number of potential problems, leaving little scope for error or inaccuracy.
Initially, I was quite confused about how I could find calculations and apply maths to a creation-based project. Even though I usually tend to have a clear understanding of the basis of a maths unit when we first begin it, this was an entirely new experience, as all my growth and learning were spread out over the course of the unit, which also meant that I made many mistakes, miscalculations, and oversights. Envisioning mathematical, numerical values to each component of the project was a bit of a learning curve at first, but nearing the end, I think I developed a rather good understanding of what to look for when creating an object, which formulas are important, which values are needed, enforcing me to see plan objects in a different light altogether: with a numerical value attached to them. If I were to do this project again, or further work on it, I would rewind a bit and think more deeply on the formulas I used, as I didn’t get a chance to fully comprehend the reason for the formula and where it’s derived from, depending on what I’m using it for. I used a plethora of formulas (e.g., surface area, volume, area, perimeter), though to achieve a more well-rounded understanding of why these formulas were employed, it would be useful to know where they come from. Furthermore, I feel that I missed a number of ‘nitty-gritty’ and tiny calculations, like incorporating different parts of the component (for example the thickness of the stickers with the lamination and adhesive, working on enhancing the design of the wheels (as the wheel wouldn’t simply be two circles, it would have a rim, an axle, and a barrel, all of which were neglected for the sake of keeping the mathematical values efficient to achieve). I also believe that a crucial part of conducting and following through on a project like this is actually designing the product, even if thats a rough draft design, it would still provide thorough insight and overview as to what is working out well and what needs to be improved (i.e. if the structure isn’t cohesively fitting together, sizing issue, material instability, cost is more than assumed, etc), and in that case the calculations and planning would likely also change.
Works Cited
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