yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Volume density


2m read
·Nov 10, 2024

In this video, we're going to talk a little bit about density, and we're especially going to talk about density in the context of volume. One simple way to think about density is it's a quantity of something, and we're going to think about examples of it per unit volume, so per volume.

For example, let's say that I have a cubic meter right over here. Actually, let me have two different cubic meters just to give you an example. So these are both cubic meters, and let's say in the one on the left I have a quantity of, let's say, six of these dots per cubic meter. And over here, I only have three of these dots per cubic meter. Well, here I have a higher density.

In general, we're going to take the quantity and divide it by the volume, and the units are going to be some quantity per unit volume. Now, you're typically going to see mass per unit volume, but density, especially in the volume context, can refer to any quantity per unit volume.

Now, with that out of the way, let's give ourselves a little bit of an example. So, here we're told that stone spheres thought to be carved by the Decay people—I'm not sure if I'm pronouncing that correctly—more than a thousand years ago are a national symbol of Costa Rica. One such sphere has a diameter of about 1.8 meters and a mass of about 8,300 kilograms.

Based on these measurements, what is the density of this sphere in kilograms per cubic meter? Round to the nearest hundred kilograms per cubic meter. So pause this video and see if you can figure that out.

All right, so we're going to want to get kilograms per cubic meter. We know the total number of kilograms in one point in a sphere that has a diameter of 1.8 meters, so that's the total number of kilograms, but we don't know the volume just yet.

So we have a sphere like this. This would be a cross-section of it; its diameter is 1.8 meters. Now, you may or may not already know that the volume of a sphere is given by four-thirds pi r cubed, and so the radius here is 0.9 meters, and so that would be the r right over here.

The volume of one of these spheres is going to be—let me write it over here—the volume is going to be four-thirds pi times 0.9 to the third power. And we know what the mass is. The mass in that volume is 8,300 kilograms, so we would know that the density, the density in this situation is going to be 8,300 kilograms per this many cubic meters: four-thirds pi times 0.9 to the third power cubic meters.

And we're going to need a calculator for this, and we're going to round to the nearest hundred kilograms. So we have 8,300 divided by—let me just open parentheses here—four divided by three times pi times 0.9 to the third power. And then I'm going to close my parentheses.

It is equal to this right over here. We want to round to the nearest hundred kilograms, so approximately 2,700 kilograms per cubic meter. 2,700 or 2,700 kilograms per cubic meter, and we are done.

More Articles

View All
Elon Musk Just Abandoned his Twitter Deal... What Next?
It was back on the 4th of April that Elon Musk first announced he was buying 9% of Twitter, a large yet relatively small ownership stake in the company. It was enough to be heard but not necessarily enough to be listened to. And to nobody’s great surprise…
AI in your life
So in this video we’re going to talk about where we all have artificial intelligence or AI in our lives. And so before I go into where we’re already seeing it and where we’re likely to start seeing it more and more, I want you to pause this video and thi…
Reid Hoffman at Startup School SV 2016
[Applause] So, uh, up next needs no introduction. I’ll give a very quick one. Reed Hoffman, uh, has been in—yeah, please do—round of applause! You know what it sounds like; you all know who he is. I’ll skip the introduction. All right, for the first que…
The Battle of SHARKS!
While riding my bike around London, I stumbled upon this and was like, “Surprise!” Sharks raise questions that need answers. So once back home, to Google I went, with a search query that would turn the next six weeks of my life real weird with phone calls…
Proof of the derivative of sin(x) | Derivatives introduction | AP Calculus AB | Khan Academy
What we have written here are two of the most useful derivatives to know in calculus. If you know that the derivative of sine of x with respect to x is cosine of x and the derivative of cosine of x with respect to x is negative sine of x, that can empower…
4 Reasons to Invest NOW | Ask Mr Wonderful Shark Tank's Kevin O'Leary
Sometimes the entire year’s return comes in just a few days, and if you’re not invested in those days, you miss out. Your 20s and 30s are prime earning years. The longer you wait, the less you will have in retirement, so it’s best you get started right no…