#mathsisfun

Outline of The Plan

According to this top result from Google, shipping via air freight would cost from 4 USD to 8 USD per kg. We’ll be using the lower bound of $4 per kilogram. But, how will we figure out the mass in kilograms?

Well, recall this physics formula:

Density = Mass / Volume

Solving for Mass gives us:

Mass = Density × Volume

So, if we knew the density of the material the ball is made of, along with the volume of the material used to make it, then we can just multiply them to get our mass. And since this image tell us the dimensions of the material (2.5 m diameter and 1mm thickness) along with the type of material used (PVC), we have almost all the information we need:

The only other information we need is the density of the PVC used, which is probably the apparently cost-effective Rigid PVC at a minimum density of 1.3 grams per cubic centimeter.

Now, given all of this, let’s look at the calculations . . . 

The Actual Calculations!

Okay, so that looks like a lot. But, let’s go through it step by step . . . 

The material is really the difference of two spherical volumes. The larger sphere has diameter 2.5 meters, and thus a radius of 1.25 meters

The smaller sphere has a radius 1 mm less than the larger one, since 1 mm is the thickness. And thus, the smaller sphere’s radius is:

Smaller Radius = 1.25 meters - 0.001 meters = 1.249 meters

The Volume of any Sphere is computed by this formula:

So, the orange bit simply subtracts the formulas for the volumes of each sphere, and substitutes the given radii. This gives us about 0.01961925 cubic meters, or converting to cubic centimeters, about 19619.25 cm^3 of plastic.

Since the density of the plastic is 1.3 grams/cm^3 (shown in maroon), this gives us about 25505 grams of mass or about 25.5 kilograms of plastic (shown in blue).

Finally, in brown, we see that even if shipping was $4 per kilogram, the shipping fee would be at least $102.

This would give us a minimum total cost of $400 + $102 shipping = $502 for the ball . . . sorry, Mabel! Even if you and Dipper did win the photo contest and split the $1000 prize evenly, you may have needed to borrow from his share! :)

Also, here’s a medal for the readers who stuck around all the way to the end: 🏅

- How easy is it to run? Very, it's a lightweight drawing tool that runs in a webpage. I've tested it on mac through safari, pc through chrome, on android phone through chrome and all ran laglessly. The only thing to keep in mind is that zoom and scroll touchscreen controls must be done outside the bounds of the drawing canvas to work.

-Can you run it in-browser? Yes! It is hosted online, is written in html (I think), and it runs on many different browsers. It also has a button for an optional flash-based version if needed/wanted.

- How easy is it to draw in? Fairly! It has two brush types (in six sizes and five transparencies), a bucket tool, polygon/shape tools, unlimited undos, clear-all, nudge, several forms of symmetry, a toggle-able grid and snap to grid tools. Two possible limitations to your drawing experience are a lack of layers and a palette limited to 31 colours, not including blending them via transparency. Erasing is also not it's own tool, but you can paint over in white, for example.

- Is it tablet compatible? Somewhat. It lacks pressure sensitivity but does detect pen/mouse/touch stroke speed, which visually affects at least one brush.

- Does it contain features that adobe would charge you money for? Considering that symmetry is something that can only be accessed through pay-for first or 3rd party plugins in most forms of photoshop, arguably yes!

- Does it do something adobe software CANNOT do (as standard)? Live updating symmetry- not just mirror-image symmetry, but a total of 13 modes of symmetry, 14 if you include the ability to turn symmetry off.

- Can it save out images or do you need to screen-grab? It can save out to .png format! As an added bonus, if you leave the default white canvas areas as-is, those areas are saved as transparency in your png. It also can connect to a printer, if you like that sort of thing.

...All in all, If you need to quickly create a symmetrical design, make a standing reference for a character or are used to working without layers, I consider this an excellent online artists resource that could probably be used to make excellent pieces of artwork. As an added bonus, while most of the mathsisfun site is dedicated to teaching math principles, there are other tools to be found, including one that produces tessellating patterns that runs in a very similar fashion.