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A Post About Maximum Surface Area


This post marks the end of another Scimatics project. This one was all about surface area,  volume, and 3D shapes. One of my favourite things to  do in math.

If you couldn’t tell, I was not trying to be sarcastic. I actually really enjoy calculating the surface area and volume of random prisms. I’m a weirdo, but whatever. We can discuss my strange interests another time.

The premise of this project was to design an inanimate object on a 3D program called Tinkercad. We either had to design the object so that it had as much surface  area or volume as possible. At first, I didn’t really understand the project. If you’re trying to get maximum volume, why not make the object the size of Vancouver? The size of Earth? It turns out that it had to be smaller that 10cm squared. That made a bit more sense.

If you read this blog often, or, in fact, any of my peers’ blogs, you may have guessed that we had a driving question for this project. You might also be a PLP teacher. That is likely the case.

How can we maximize the surface area or volume of an object?

So, basically what I just explained.

Given Mr. Gross’s desire for short blog posts, let’s get right to the point (she said, after writing a 4 paragraph introduction).

The standard 3 Curricular Competencies:

  • Reasoning and Analyzing
  • Applying and Innovating
  • Communicating and Representing

Cool. Let’s begin.

I decided at the beginning of this project that I wanted to create a slide, with maximum surface area. I was randomly fiddling around with Tinkercad when I had that stroke of inspiration.

Side note: before this project, I had never used Tinkercad, or any sort of 3D modelling software for that matter. I had seen my sister working with it, though, so I used my limited knowledge of the program to make random objects. That’s how I figured out about the slide.

After working on the slide some more, I realized that I definitely did not had the required 10 shapes. I added one of those spinny merry-go-round things to make a full-on playground.

Here is my final creation:

I think it turned out well. After this screenshot was taken, I added a base so that the pieces would stick together when we 3D printed them.

Next I had to calculate the surface area and volume of my creation. It took me so long to calculate it all, but eventually I was finished and left with this chaotic mess:


I later made a more legible good copy to hand in.

Finally, I calculated the surface area-to-volume ratio. Drumroll, please…

It didn’t work out exactly as planned, but what can you do? Whatever kid is going to play on it won’t care, anyways.

Now I suppose I should be getting on with the Curricular Competencies.

Reasoning and Analyzing: Model mathematics in contextualized experiences.

I used Tinkercad to make a playground 3D model, which included 17 shapes. I attempted to optimize my design for surface area, but didn’t exactly succeed. I could have made the pieces thinner and longer for more surface area. Oh well, at least I know where I went wrong.

Applying and Innovating: Contribute to care for self, others, community, and world through personal or collaborative approaches. 

For this competency, I think I did pretty well. Better than usual, in fact, because I did not feel the need to take repeated breaks, like in some other projects. I also complete all the required workbook pages relatively accurately.

Communicating and Representing: Explain and justify mathematical ideas and decisions.

I calculated the surface area and volume of all my shapes precisely and accurately. My ratio isn’t what I hoped it would be, but at least it’s correct! My Keynote presentation includes images of my design, clearly shows the calculations that I made to determine the surface area and volume, and the ration was displayed visibly and prominently at the end.

So I guess that’s it!

I am in the process of writing 2 other posts before spring break. Hopefully they will be out before Friday, since that’s when they’re due.  A busy time for this blog!

Evelyn 👩🏽

1 Comment

  1. Great job! I like some of the examples about using field experience such as their vacation and random acts of their personal lives that they can share to put in their backpack.

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