A die is basically a cube. Calculate density by measuring the volume of the cube and dividing that into the weight of the cube.
The volume can be calculated using the formula for a cube. Let's assume the holes in the faces are negligible. All three sides of a cube(Length, width and height) are the same length.
Volume = length of side X length of side X length of side
Measure the weight of the die.
Density = Weight / Volume
If the dots on the die are cut out, then you can get a little more accurate by measuring the size of the dot and calculating the depth. Then you would try to calculate the volume of a dot on the die.
Then subtract this volume for each of the dots on the faces of the die. There are 21 dots(I think).
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