Maths Quiz.

[M600]

FIRST OFF

the balls will be arranged in between each other as in the diagram below to allow more space





the balls will have a certain number going across as you can only fit so many going along the x plane, since this is a cube the x and z will have the same amount of balls, the y axis however will be will have more as the balls going upwards will be zig zaggin along since the balls will be stacked in between each other as in figure one
the example amount i will use is a 5 by 5 box, so 5 balls across x and z on the first level
on the second level there will be a 4 by 4 grid as to put the balls in between on the second level on will have to be sacrificed by x and z
on the third level there will be a 5 by 5 grid again and on the 4th a 4 by 4
so the easiest way to work this out is to do the first 2 levels and multiply them by the overall length
to do this we need to work out the height of the segment which is hidden in between the balls on the second level, or how much height we save by putting the ball in between
here is a diagram




we do this by finding the length x of the triangle, do this by suing the equation
1.25 sin 30 = 1.23503953
minus the answer by the radius to get the height of the segment which is 0.01496 mm

so now the height of 2 levels is 5mm - 0.01496mm = 4.98504mm

divide that amount by 1m height 1000 / 4.98504 = 200.6

so there are 200.6 sets of 2 levels stacked upwards so 401.2 balls up

now to work out z and x

1000 / 2.5 = 400

first level amount = 160 000

second level amount = 399 x 399 = 159 201

so in the first 2 levels we have 319 201

we know there are 200.6 sets of 2 levels

so 200.6 x 319 201 = 64 031 720.6

or 64,031,720 balls

cant be bother to work out volume, jsut work out the volume for one and times it by the amount

 

[Skeet]

FIRST OFF

the balls will be arranged in between each other as in the diagram below to allow more space





the balls will have a certain number going across as you can only fit so many going along the x plane, since this is a cube the x and z will have the same amount of balls, the y axis however will be will have more as the balls going upwards will be zig zaggin along since the balls will be stacked in between each other as in figure one
the example amount i will use is a 5 by 5 box, so 5 balls across x and z on the first level
on the second level there will be a 4 by 4 grid as to put the balls in between on the second level on will have to be sacrificed by x and z
on the third level there will be a 5 by 5 grid again and on the 4th a 4 by 4
so the easiest way to work this out is to do the first 2 levels and multiply them by the overall length
to do this we need to work out the height of the segment which is hidden in between the balls on the second level, or how much height we save by putting the ball in between
here is a diagram




we do this by finding the length x of the triangle, do this by suing the equation
1.25 sin 30 = 1.23503953
minus the answer by the radius to get the height of the segment which is 0.01496 mm

so now the height of 2 levels is 5mm - 0.01496mm = 4.98504mm

divide that amount by 1m height 1000 / 4.98504 = 200.6

so there are 200.6 sets of 2 levels stacked upwards so 401.2 balls up

now to work out z and x

1000 / 2.5 = 400

first level amount = 160 000

second level amount = 399 x 399 = 159 201

so in the first 2 levels we have 319 201

we know there are 200.6 sets of 2 levels

so 200.6 x 319 201 = 64 031 720.6

or 64,031,720 balls

cant be bother to work out volume, jsut work out the volume for one and times it by the amount

Did you see my post then?

 

[M600]

lol no i didnt, it seemed too long and lacked awesome pictures
we got different answers though
the first layer should have 160, 000

 

[MsHell]

FIRST OFF




we do this by finding the length x of the triangle, do this by suing the equation
1.25 sin 30 = 1.23503953

I haven't checked the rest of your calculations however there is a big flaw in this calculation. Angles in a triangle sum to 180 degrees and currently yours add up to 150. The bottom left hand corner should be 60 degrees.

Hence your calculations for x should be
1.25 sin 60 or 1.25 cos 30

 

[Skeet]

the first layer should have 160, 000

Really? Why?

Do the rows not fit into each other, in the same way as the levels do then?

Go look again.

Also, you can't have 0.6 of a level etc, if that 0.6 puts it outside the confines of the box, and you can't have 0.6 of one or many bearings. Not in that context.

 

[MsHell]

sh*tloads.

I think this was the best answer though

 

[Cook$]

This is gay. Balls are touching.

 

[Skeet]

This is gay. Balls are touching.

It's only Gay if they look into each others eyes....or swallow.

 

[Cook$]

For all you newer guys who don't know Skeet, he's like the Halley's Comet of sexual innapropriateness. He appears every so often, says something filthy, then dissapears off into the blackness leaving everybody open mouthed and squinting.

 

[Skeet]

For all you newer guys who don't know Skeet, he's like the Halley's Comet of sexual innapropriateness. He appears every so often, says something filthy, then dissapears off into the blackness leaving everybody open mouthed and squinting.

I love you.

I don't think they know me. They seem to be ignoring the appropriate things I have said in this thread.

Anyway...you started it