Origami Cup Volume (cont) by

Scott Keita Okamura, on Flickr

Found a way to calculate the volume of this cup.

The way I did it was to divide the cone shape into pieces shown in the top section. So,

Cup = Cone - 4*Big + 2*Small

To find the 'big' and 'small' shapes' volumes, I used the same formula as volume of a cone/pyramid:

V = (1/3)*(Area of base)*(height)

I was able to find the area of the base by doing Integration on the equation of the ellipse: x^2/a^2 + y^2/b^2 = 1. And to find a, b, and h, geometry(mostly trigonometry due to all the triangles) was used.

For a 20cm square: 155.463mL(Finally done! I hadn't done math lately but got to do some interesting math, so Thanks Gerardo for the interesting question!

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