- #36
maline
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Oh, now that I finished my post I saw's Nidum's new beautiful diagrams. Yes, that's what I mean by "prongs". Too bad it's hard to see that their cross-section is square.
Thank you!
Thank you!
That's right.Nidum said:The cross section of anyone wing at any point along the length is square and the function defining the edge length is a simple geometric one ?
PhysicsOfLearning said:The volume leftover from the drill holes in the square is:
2.654÷2.54 = 1.044 cubic inches of cube left over.
Is that correct?
PeroK said:Given that the original cube only has a volume of 1 cubic inch, probably not!
Cubing an area does not give a volume.
PhysicsOfLearning said:Oops!
Methodology wrong as well?
The integrals actually can be computed in closed form to give ## V=1+\sqrt{2}-\frac{3}{4} \pi ##. It might interest you that you can also get a numerical answer with about 15 lines of computer code using 3 nested For-Next loops ("Do" loops) that divide the volume into 100x100x100 parts and using inequalities to test whether a point (tiny cube) lies inside or outside the 3 cylinders. If it lies outside the 3 cylinders, you count ## N=N+1 ##. Once the "Do" Loops have completed all 1,000,000 points, you compute ## V=N/1,000,000 ##. With 1,000,000 points (100 intervals on each Do Loop), you can get an answer accurate to about 3 or 4 decimal places or more.JasonWuzHear said:okay I have my answer, the volume of what's left of the cube is...0.0580191... in^3here's an imgur album with my work:
http://imgur.com/a/Xzwjk
agh forgot to say that the 4 pi r^2 should be a pi r^2 obviously. When I evaluated the integral numerically in mathematica I fixed it. Seems I got the right answer from reading the past pages, but less efficiently.