# Can you estimate the diameter of a really giant ball of cheese?

The current U.S. cheese stockpile is 1.39 billion pounds, or about 4 pounds for every man woman and child in America. Without doing any research or math, which poll number comes closest to your estimate of the diameter of a cheese ball made from all that cheese?

Cheese is pretty heavy.

No poll options are visible yet, but with a bit of mental math and reasonable approximation, it’d be in the vicinity of 100 m diameter.

There is a great visualization in this article, which inspired the thread, so I’m spoilering it for people who want to guess without reading first.

My guess was about one option away from the correct poll answer.

Agreed. Since the cube root of a billion is thousand, 330’ seems right.

Now that the poll is there, my initial guess was 1,000’. Then I read the thread. I still went with 1,000.

It’ll be interesting to see what it is.

If I did that and lifted, I might cut some cheese. Don’t stand downwind!

My approximations:

1.4 billion lb is about 600 million kg, or 600,000 metric tons. Cheese has about the same density of water. A metric ton of water is 1 cubic meter. So 600,000 cubic meters. Volume of a sphere is 4/3 Pi r[sup]3[/sup], so r[sup]3[/sup] is about 150,000, 10 cubed is a thousand, 5 cubed is 125, so r is a little more than 50 meters, and diameter is about 100 m, or 330 ft.

The Vox article is wrong. They list the meat stockpile as being less than twice the cheese stockpile, and meat and cheese have similar densities, but they show it as being about fifty times the size of the cheese stockpile.

My estimate:

1.39 billion lb is a bit less than 1 billion kg, or 1 billion liters in volume (because density should be close to 1). A liter is 0.1m cube, so that’s a 100m cube, i.e. 300 ft. A sphere is a bit smaller than a cube it fits in, but not by much. So chose whatever is closest to 100m.

My guess was 1,000 feet, but I didn’t have anyone to offer my barometer.

It would depend on the cheese. Swiss would have volume than Cheddar.

The correct answer is becoming apparent, based on the responses. I’m trying to visualize a ball of cheese with a D of those answers, and yeah, I can imagine it weighing 1.4 billion pounds.

I don’t endorse the meat graphic, which is very wrong. The cheese graphic looks right to me and I thought it was very interesting. I independently calculated the cheese volume and came up with something in their scale. I should have mentioned that the meat graphic was bad but I was more interested in my own overestimate of the size of the cheese ball.

No math or research, 1000 feet seemed too big and 100 feet not big enough. Looks like that was the answer anyway. If a few more numbers less than a 1000 were in the poll I wouldn’t have picked something like 500 feet.

I may have gone a size too large. Don’t let the ELCA know that (or the fact that I own several bottles of pepper sauce) or I may be thrown off the roster.

Should we bring Sisyphus out of retirement to deal with this?

The poll size distribution made me wonder if I misplaced a zero or exponent. Anyway, doing this all in my head: 1.4 billion pounds is about 6 hundred million kilos. Ish. It’ll get messier from here. I guestimated that cheese floats so 1 g/cc. 6E11 kilos is 6E14 grams. Volume of a sphere is 4/3pir^3 and dividing 6E14 by first 4/3 then by pi, I get around 1.5E14 The cube of 1E4 is 1E12 and the cube of 1E5 is 1E15, so the cube root of 1.5E14 is going to be in between those. 5 cubed is 125, 6 is 216, so I took 5.5E4 as the radius and called it a day. 55,000 cm is 550 m for the radius, or 1100 m for the diameter. Which is close enough to 3300 feet.

I haven’t gone through the rest of your numbers, but it’s 6x10^8 kg, not 6x10^11kg.