**UNFINISHED**

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