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Origami Cup Volume (cont) | by ShuaiJanaiDesu
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Origami Cup Volume (cont)

Continuation from previous picture (sort of). I only listed the results and did not include all of the formulas and calculations due to space (and due to laziness)

 

I found the volume of the cup by dividing the cone shape into pieces shown on the top section of the picture.

 

The pieces that I call "big" and "small" are basically cones/pyramids with a semi-ellipse base. So I can find these volumes by V = (1/3)Area * height.

 

To find the Area of these semi-ellipses, I use integration. But to find the equations of the ellipses, I used geometry.

 

Hopefully, there are no input errors(since the equations/formulas became quite long) but if so, the answer came out to be 65.586mL for a 15cm square

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Uploaded on July 24, 2016