How Well Can You Compute?

[Gregory Matthews]

For the answer to the following see:

http://www.scientificamerican.com/video/epic-math-battles-lego-versus-trees/

Question:  If you were to build a full-scale copy of the Great Pyramid out of Legos, which would be greater, the number of Legos required, of the number of trees growing on the Earth?  To help you to determine the correct answer, pick from the following for the number of Legos, one of which is correct:

372 Million

1.75 Billion

540 Billion

740 Billion

1.4 Trillion

NOTE:  Click on and watch  the video and you just might learn something.

 

 

 

 

[Bravus]

I admit I had to look up the size of the pyramid, because I didn't have a real sense of the scale.

Square pyramid, 230 m on a side and roughly 140 m tall. The volume of a square pyramid is the cube of the side length times 1/3 the height, so 230³ times 140/3 = 567,793,333 cubic metres.

Now, an average base Lego block is about 1 cm by 3.2 cm by 1.6 cm = 5.12 cubic cm. There are 100 cm in a m, so 100³ cm³ in a m³, so we divide this by 1,000,000 to find the volume of a Lego block in cubic metres: 5.2x10^-6 m³.

Dividing the volume of the pyramid by this gives: 1.09x10¹⁴ blocks required, which is about 100 trillion blocks.

This is not on Gregory's list, and is larger than any of the numbers there. There is likely to be some estimation error there somewhere, e.g. imagining using Lego blocks other than the base block.

This seems to me to be a much larger number than the number of trees on earth. That's a much harder estimation, but as a very rough guess, say that there is 1 tree per square metre on the dry-land parts of the earth. The radius of the earth is about 6400 km or 6.4x10^6 m. The surface area of a sphere is given by 4 pi times the square of the radius, so the whole surface area is about 514 trillion square metres. Of that, though, 70% is covered by oceans, so the remaining 30% is only 154 trillion square metres.

Using my assumptions, the two numbers are on the same scale, so quite comparable: and there are so many shaky assumptions that I wouldn't feel really confident picking one over the other. If even the largest of Gregory's numbers is correct, though, I'd say there are more trees than Legos.

Now to watch the video.

[Bravus]

Aahhh... picked the wrong formula for pyramid volume! I should have known: the cube of the side length times the height would be m⁴ and I need m³. Basically, I just need to divide my final answer by the side length, 230 m, which gives 473 billion, not a million miles from the 540 billion in Gregory's list and the video... and well short of the number of trees.

That's true even though I massively overstimated the number of trees, by about 50 times. I guess the amounts of land that are Antarctica and deserts and plains and so on pulled the average a lot lower than one tree per square metre.

[Gail]

Whizzzz...... (not entirely over my head, but your knowledge of math is appreciated)

[Outta Here]

There aren't enough Lego bricks in the world to build a pyramid that size...not yet. Almost. But not yet. Give it a minute.