# Building Farm Animals : the Formulas Behind the Magic

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Have you ever wondered how math whizzes do it? Find the additive inverse of a matrix? Graph a tautochrone? This tutorial will show you exactly how to become one, and also have some fun in the process!

### Supplies:

3D Printer

Knowledge of the volume of your animal

Filament

Pencil

Paper

### Teacher Notes

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## Step 1: Measurements

Start with a cylinder. This will be half of the volume, and the height is twice the radius, so to find the radius of the cylinder, use this formula:

r= cbrt( v/(4pi))

Or, radius is the cube root of the quotient of the volume and 4pi, which is 12.56. Mine is volume 100,000, which just so happens to be about 20 and 40.

## Step 2: Legs

The general legs are cylinders. Feet have almost no volume at all so we will say each radius of the cylinders are 1/3 of the big one's radius. The height is half. Then, for the front legs use a 20*20 cylinder and put a 1 cm by 20 cm by 20 cm hole in the center. The picture is bottom view.

## Step 3: Head Part One

Let's design the head shape. We've used half the volume for body, and about 1/5 for the legs. This means we still have 3/10 of the volume for the head. For the head shape, we'll use a hemisphere.

Use this formula:

D= 2cbrt2 * (3v/12.56)^1/3

Or 2 cube root of 2 times the following: quotient of 3 times the volume of the sphere divided by 12.56 and then only the fraction raised to the 1/3 power. This is your diameter. Don't worry if the head is bigger than the cylinder, you can just make each closer to the average so they are about the same.

## Step 4: Head Part Two

Now subtract a triangular prism or roof with a hole. This step requires no calculations, except finding the volume and subtracting it from our total.

## Step 5: Head Part Three

Use small different colored spheres for the eyes. You can also use the scribble tool like I have.

## Step 6: All Done! Now Add a Tail and Color!

Just use another scribble. You can attach it wherever you like. Not all the pieces have to be the same color.

Use the remaining volume for food, accessories, clothes, or anything else.

So cute!!!

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