I have a "block" that is 2.61 inches wide, 6.14 inches long and 4.3 inches tall.

That is what a stack of one thousand one dollar (US) bills looks like. I understand that it is 69 cubic inches.

I'd like to get a mental picture of what one thousand of those "blocks" would look like when arranged as close to a "cube" as possible.

What is the formula for how that works?

I do understand that one thousand of those blocks would be about 69,000 square inches. What I'm looking for is how to show what 69,000 inches looks like as close to a cube as possible.

So in short, how many inches wide, long and tall will 1000 "blocks" be, reduced to as close to a "cube" as possible?

Thanks!

To find the length of each side of a cube given the volume you take the cube root:


\sqrt[3] {69,000 \ in^3} = 41\ in

If you want to be more precise than that, the volume is 68.9 in^3

1000 of those, and you get 68909.2 in^3

cube root of that gives you 41.0 in

that's assuming the blocks form a perfect cube.

Placing each block side by side in an 'orderly manner', you'll get

41/2.61 = 15 along the width (39.15 in)
41/6.14 = 6 along the length (36.84 in)
41/4.3 = 9 along the height (38.7 in)

But that doesn't make 1000 blocks.

Adding a 'sheet of blocks' to make the length longer, adds 15*9 = blocks 135 blocks and the width is now 42.98 in

Total blocks now is 945

you can add some more to get the height bigger, but that means you have to add 9*7 = 63 blocks, which would then exceed 1000 blocks.

So, final 'properties':
15 along the width, 39.15 in
7 along the length, 42.98 in
9 along the height, 38.7 in

You could add some more blocks, but the result would be less 'cube':
16 along the width, 41.76 in
6 along the length, 36.84 in
10 along the height, 43 in
which takes 960 blocks.

Thank you, ebaines and Jerry!

I'll work out the math and then post my project here, so that the two of you can evaluate it and be sure that I did it right.

Here's a good visualization too. Maybe you already say this? Either way, it's a good way to drive the point home:

http://www.pagetutor.com/trillion/index.html

Here's a good visualization too. Maybe you already say this? Either way, it's a good way to drive the point home:

http://www.pagetutor.com/trillion/index.html

Yes, I did see that link. My project is using one dollar bills, rather than one hundred dollar bills, like the above link shows.

Thank you, jcaron2.

This shot from the web site http://www.pagetutor.com/trillion/index.html of $100 million made with $100 bills is exactly equivalent to $1 million made with $1 bills, which is what you asked about. Note that it's a cube about 41 inches on each side, as previously explained.

This shot frm eth web site What does one TRILLION dollars look like? (http://www.pagetutor.com/trillion/index.html) of $100 million made with $100 bills is exactly equivalent to $1 million made with $1 bills, which is what you asked about. Note that it's a cube about 41 inches on each side, as previously explained.

Yes, I understand that relationship. Thanks, ebaines!

Your post got be thinking about this.

A trillion one-dollar bills would be enough to fill 11 Super-Walmart stores from floor to ceiling (assuming a 20-foot high ceiling)!

Also, you could fill every single office in the Pentagon from floor to ceiling (assuming a 10-foot ceiling).

Or you could fill 40% of the volume of the Dallas Cowboys' Stadium!