In the episode, Plaza Film Festival, the Boxmore Robots win the festival and receive a Plutonium trophy as a reward, much to the Bodegamen's dismay. And despite their best, they failed poorly and the trophy exploded. Which leads us into his calculation.


Finding Dimensions

To start it off, we need to find the volume of the trophy, which requires the dimensions of it.

In one panel, we can easily find the width and the height of if, comparing it to Radicles, who was in the same frame.

Live and Learn 1

The average height for 16-year-old boys range from between 5 feet, 3 inches to 6 feet, 2 inches. The average of that is 5 feet, 8.5 inches, which is 1.74 meters tall.

In the image above, we can see that Rad stands at 97.23 px (1.74 m) meaning that it's 1 meter for every 55.88 pixels.

The height of the trophy is 30.03 px (0.54 m), and the width is 36.62 px (0.66 m), which is ⅔ of what we need to find the volume.

Luckily for us, there is another frame to find it.

Live and Learn 2

Assuming that Darrell's head is average human head size, since it appears the most humanoid with a brain to go with it, with his head being 138.14 px (0.239 m), the ratio for this image is 1 meter for every 577.99 pixels, which none of these are.

The length of the trophy is 30.82 px (0.53 m).

And with that, we have all of the dimensions.

Finding Volume/Mass

For simplicity, we'll use the rectangular tank volume formula, which seems the most likely.

The volume is simply lwh, or length * width * height where length = 0.53, width = 0.66, and height = 0.54. It's pretty simple math to follow with a calculator.

0.53 * 0.66 * 0.54 = 0.189 m^3

0.189 * 1e+6 = 189000 cc

And now that we have that, we can find the mass of the trophy. The density of plutonium is listed on Wikipedia as 19.816 g/cc which makes this so friggin easy.

19.816 * 189000 = 3745224 g

And 3745224 / 1000 = 3745.224 kg

Heh, casual Class 5.

Finding Destructive Capacity

The trophy is 3745.224 kg and a research on the Fat Man bombs have brought up that 6.2 kg worth of plutonium is equal to 20 Kilotons of TNT. That's just quick math.

20 Kilotons of TNT is 8.368e+13 Joules, by the way.

So, 3745.224 / 6.2 = 604.07x the explosive yield

8.368e+13 * 604.07 = 5.0548578e+16 J


The result is 5.0548578e+16 J (12.08 Megatons; City level), which scales to the main Season 2 characters and the people they face along the way. This also appears to be a casual durability feat since they weren't really in battle at the time.

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