I was partnered with my friend Cameron!
Milestone one: driving question
So the first thing that we did was we actually MADE our driving question! Our teacher gave us a template, “How can I design a _________ for maximum surface area/volume?” And then we had to fill in the blank, this is what we decided to do: “How can I design a pizza and pizza box for maximum volume?”
Originally, we were going to make a circular pizza box, but then we decided that that would be to hard, so we went with a pizza! And then we decided we’d also make a pizza box, but it wouldn’t be circular lol
As usual, we all went and did a buncha workbooks, and then FINALLY, we would get to the good stuff!
Milestone 2: model and formulas
I didn’t do this very well I don’t think, I misunderstood the assignment and then didn’t know how to fix it, so I just left it as is. I did get a ⛅️/☀️ Which isn’t horrible, but I can probably do better next time…
anyways, here’s what it ended up looking like :))
Milestone 3: calculations
so, I’m going to be honest here, I didn’t do a lot of the work for this assignment, it was mostly cam, I didn’t know that we were supposed to do individual calculations. I mean, I did note down all the measurements for the pizza and pizza box, although he took those measurements and calculated the surface area, volume, ratio, etc.
heres what it ended up looking like (sorry for the endless wall of math lol)
Scimatics Design Challenge
Surface area
PIZZA
Top of pepperoni A=πr2=π·1.912≈11.401 x 7 = 79.807
Side of pepperoni
C=2πr=2·π·1.91≈11.969 x 0.1 = 1.197 x 7 = 8.379
Pepperoni 79.807 + 8.379 = 88.186
Top of Cheese A = πr2 = π·11.052 ≈ 383.457 – 79.807 = 303.65
Bottom crust A = πr2 = π·11.052 ≈ 383.457
Pizza 88.186 + 303.65 + 383.457 = 775.293
Volume
PIZZA
Pepperoni V = πr2h = π · 1.912 · 0.1 ≈ 1.14 x 7 = 7.98
Cheese V = πr2h = π · 11.052 · 0.3 ≈ 113.887
Bottom Crust V = πr2h = π · 11.252 · 0.89 ≈ 354.269
Ring of Crust V = πr2h = π · 122 · 2.38 ≈ 1074.425 – 944.319 = 130.106
Pizza 7.98 + 354.269 + 113.887 + 130.106 = 606.242
Surface area
PIZZABOX
Top of Bottom of box 27 x 27 = 729 – (13.5 x 2 + 26 x 2) = 650 (squared)
Sides of bottom of box 27 x 0.375 = 10.125 x 4 = 40.5 (squared)
Bottom of box 27 x 27 = 729 (squared)
Bottom of box 650 + 40.5 + 729 = 1419.5
Top of front wall .5 x 27 = 13.5 x 2 = 27 (squared)
Front of front and back walls 27 x 2.5 = 67.5 x 2 = 135 (squared)
Back of front and back walls 27 x 2.5 = 67.5 – (2.5 x 2) = 62.5 x 2 = 125 (squared)
Right and left of front and back walls 0.5 x 2.5 = 1.25 x 4 = 5 (squared)
Front and back walls 27 + 135 + 125 + 5 = 292
Top of Left and right walls 1 x 26 = 26 x 2 =52 (squared)
Left and right of left and right walls 26 x 2.5 = 65 x 4 = 260 (squared)
Left and right walls 52 + 260 = 312
Bottom All flaps 0.2 x 26.576 = 5.3152 x 3 = 15.946 (squared)
Right and left of all flaps (front and back for front) 26.576 x 1.284 = 34.124 x 6 = 204.744 (squared)
Front and back of all flaps (left and right of front) 0.2 x 1.284 = 0.257 x 6 = 1.542 (squared)
All flaps 15.946 + 204.744 + 1.542 = 222.232
Top of top of box 27 x 27 = 729 (squared)
Sides of top of box 27 x 1 = 27 x 4 = 108 (squared)
Bottom of top of box 27 x 27 = 729 – (5.3152 x 3) = 713.036 (squared)
Top of box 729 + 108 + 713.036 = 1550.036
Pizza Box 1419.5 + 292 + 312 + 222.232 + 1550.036 = 3795.768
Volume
PIZZABOX
Front and back walls 0.5 x 27 x 2.5 = 33.75 x 2 = 67.5 (cubed)
Right and Left walls 26 x 1 x 2.5 = 65 x 2 = 130 (cubed)
Bottom of box 27 x 27 x 0.375 = 273.375 (cubed)
All Flaps 0.2 x 26.576 x 1.284 = 6.825 x 3 = 20.475 (cubed)
Top of box 27 x 27 x 1 = 729 (cubed)
Pizza Box 67.5 + 130 + 273.375 + 20.475 + 729 = 1220.35
Milestone 5 (there wasn’t a milestone 4 for some reason): presentation
Our presentation ended up going really well!! A lot better than I thought it would, I would import the video of Cam and I presenting, but I forget how to TwT
I wish that we had practiced a little more, I was stuttering a lot and needing to constantly look at the presentation to read the words, instead of making eye constant with my audience, I will certainly do better on that next time.
Anyways, if anyones interested, here’s our presentation!!
Milestone 6: blog post
I don’t have much to say on this one since you know, you’re reading it right now!!
IT’S TIME FOR THE MOMENT YOU’VE ALL BE WAITING FOR!! The answers the the driving question!!
Question: “How can I design a pizza and pizza box for maximum volume?”
Answer: Well, we didn’t actually end up meeting our goal, which was to maximize the volume, id say that the pizza is probably maximizing the volume, but it was probably the pizza box that messed it up a little. We could’ve made the walls a lot thicker, which yes, would increase the surface area, but it would increase the volume even more.
Thank you for reading my blog post!! I hope y’all will have a lovely day <33