- [Instructor] In this video,
we're gonna talk a little bit about density
and we're especially gonna talk about density
in the context of volume.
And 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.
So 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 and in general,
we're gonna 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 Diquis 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 masses 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.
So we're gonna want to get kilograms per cubic meter.
So 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 4/3 PI R cubed.
And so the radius here is 0.9 meters.
And so that would be the R right over here.
So the volume of one of these spheres is going to be...
Let me write it over here.
The volume is going to be 4/3 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,
8,300 kilograms per this many cubic meters,
4/3 PI times 0.9 to the third power cubic meters.
And we're going to need a calculator for this
and we're gonna round to the nearest hundred kilograms.
So we have 8,300 divided by,
let me just open parenthesis here.
Four divided by three times PI
times 0.9 to the third power,
and then I'm going to close my parentheses,
is equal to this right over here.
We want to round to the nearest hundred kilogram.
So approximately 2,700 kilograms per cubic meter,
2,700 or 2,700 kilograms per cubic meter.
And we are done.