Many of my questions come from my kids. As we were cleaning up leaves, we pushed all the leaves from one tree into a corner. My daughter asked me to estimate the number of leaves in the pile (yes, she is going to be a great blogger one day). Are there a million leaves in the pile? My off the wall guess was: no, not a million. However, I really don't know if I am totally off or not.
To get a better estimate (at least better than a wild guess), I took a small sample of leaves.
With this sample, I can count the number of leaves. I can also estimate the volume of this small pile to get the leaf volume density (leaves per cubic meter). So, how many leaves? It might not look like it, but this is 50 leaves. How big is this pile? Let me estimate that this pile of leaves is a sphere (spherical leaf pile) with a radius of 7 cm. The volume of this pile would then be:
This gives a leaf-density of (not to be confused with mass density even though I will use the same symbol):
I can already see that there are not one million leaves in the pile. At that density, I would need on the order of 50 cubic meters of leaves. Yes, this is still an estimate - there are lots of things that could be off, like the leaf density itself. However, it probably won't be off by that much. Ok, let me finish the estimate and then we can talk about limitations.
How big is the pile? You can see in the image at the top, the shape and size of the pile of leaves. For an approximation, I will say that this pile is in the shape of a quarter of a cone. The radius of the pile is about 2 meters with a height of around 1 meter. The volume of a cone is:
Just to be clear, the h is the height of the cone. Using my values, one fourth of this cone volume would be 1.05 m3. Remember, this is just an estimate. But there are limits to this estimate. Sure, the volume isn't EXCACTLY 1.05 cubic meters. However, I don't see the volume of leaves being less than 0.5 or more than 3 cubic meters.
Now for the number of leaves. Let me start off with my first guesses for the leaf-density and the volume of the pile. With the leaf-density formula, I have:
Not a million leaves, just 30 thousand leaves. Ok, maybe I made a bad assumption about the leaf density. Maybe the leaves at the bottom of the pile are super smashed into an almost black hole-like density. Would it make you happier if I used a density 3 times has high as my estimate? This would give a number of leaves at just over 100 thousand. There is no way there could be a million leaves in that pile.
But how many leaves does the tree have? Just by looking at the type of leaf, it looks like almost all of the leaves came from this tree.
Perhaps just 5% of the leaves are still on the tree. Some might have fallen off and blown to a location such that they didn't end up in the pile and some might have been collected by an 8 year old who wanted to use leaves for an art project. Overall, I would say that there could be from maybe 30 to 50 thousand leaves on that were originally on the tree.
