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TimeSpaceLightForce

Cutting corner

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1. Cut the sheet into 5 congruent rectangles.

2. Cut&weld each rectangle into a square.

3. Weld 5 squares together into an open top box that can hold (1/5)^(3/2) = 0.0894 m^2 of liquid (more than 89 liters).

That is right! Nice 1

post-53237-0-86864200-1375899003_thumb.j

But the maxima solution and the rectangle to square method are under and over design for fabrication.

The 9 grids solution is enough for the problem.

post-53237-0-72470300-1375899517_thumb.j

For the best.. i got the idea from witzars solution..

post-53237-0-94228900-1375899889_thumb.j

Edited by TimeSpaceLightForce

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Im trying to edit the weld value of Greek cross solution to 3.788m , this make it cheaper for 9 grids solution to fabricate

note: pls hide last figure

Edited by TimeSpaceLightForce

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My instincts tell me that half a sphere would give you best results.

In this case if you can make half a sphere with area of 1 M2 you'd have space for 94 liters.

But since you can't make a perfect sphere by cutting and welding, you can try to make it close to a sphere by making a polygon of the highest order as you can, the higher the order the more pieces you'll have to cut and weld

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Roll sheet into a cylindar that will have the volume of 1 meter times area of opening (Circumference of 1 M)

1)For height=circumference:no base

V=h (a) volume

h=C=1 height

C=piD=1 circumference

D=2r=(1/pi) diameter

r=1/2/pi radius

a=pi(r )^2 circle area

V=(1)(pi)(1/2/pi)^2

V= 0.07958

2) For height=diameter :no base

a=pi( r)^2 circle area

D= 2r=(C/pi) diameter

r=C/pi/2 raduis

A=1=2rC cylinder area

C=1/2/r circumference

r=(1/2/r)/pi/2

r=0.28209

V=2r(pi)r^2 volume

V=0.14105

good for holding marbles

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My instincts tell me that half a sphere would give you best results.

In this case if you can make half a sphere with area of 1 M2 you'd have space for 94 liters.

But since you can't make a perfect sphere by cutting and welding, you can try to make it close to a sphere by making a polygon of the highest order as you can, the higher the order the more pieces you'll have to cut and weld

1) volume of sphere=4/3 (Pi) rrr

area of sphere=4(pi)rr

1=4(pi)rr

r=0.28209

V=0.09403

2) volume of half sphere=2/3 (Pi) rrr

area of half sphere=2(pi)rr

1=2(pi)rr

r=0.39894

V=0.13298

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My instincts tell me that half a sphere would give you best results.

In this case if you can make half a sphere with area of 1 M2 you'd have space for 94 liters.

But since you can't make a perfect sphere by cutting and welding, you can try to make it close to a sphere by making a polygon of the highest order as you can, the higher the order the more pieces you'll have to cut and weld

1) volume of sphere=4/3 (Pi) rrr

area of sphere=4(pi)rr

1=4(pi)rr

r=0.28209

V=0.09403

2) volume of half sphere=2/3 (Pi) rrr

area of half sphere=2(pi)rr

1=2(pi)rr

r=0.39894

V=0.13298

Yes, the volume is in units of meter3, 1 m3 = 1000 liters.

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