In this video we get to take a look at what "volume" is.
And a definition would be:
So let's take a closer look at that definition and how we measure such things as volume. And you may notice, if you look around wherever you happen to be, that just about everything you're looking at has three dimensions.
It has height, it has width, and it has depth.
It doesn't have to be a regular shape like a box. It can be anything that has space within it. And the space doesn't have to be empty. It can be occupied with anything.
So, if it's a regular shape, we can simply calculate the space occupied by a box by simply measuring each side.
So here we have three examples. For example, here we have 4 cm on one side, 2 cm on another.
And 5 cm on the third.
So height, depth, and width.
And if we look over to the right here, we can see that this is a cube that has a measurement of 1cm on each side.
So measuring the amount of space occupied by this cube, we would have 1 cm as the height, 1 cm as the depth, 1 cm as the width.
And so that gives us 1 cubic cm of space.
We've multiplied 1 cm by itself three times. 1 cm x 1 cm x 1 cm.
So if we look at the box, the same idea applies, where we simply multiply the height times the width times the depth.
So the question is, how many of these single cubic centimeters fill a box with a height of 4 cm, a length of 5 cm, and a width of 2 cm.
Well, let's take a look. So we'll bring the cube over and see how many fit the length of it.
We've measured 5 cm, so we would expect five 1 cubic centimeter boxes to fit across the length.
Let's look at the width. How many 1 cubic cm boxes would fit across that width?
Well, you guessed it, 2. But we still have the 5 cm length so we would fill that up with a total of 5 boxes.
And now what's left is the height, 4 cm. So the question is, how many 1 cubic cm boxes would fit a height of 4 cm and we already have one so a second, a third, and a fourth, and we've already filled in the length with five boxes.
And now we have the width of 2 cm left to fill in. So we have the first five, the second five, the third five, and the fourth five.
And so what we've done is fill up the box with as many 1 cubic centimeter cubes as we can.
And what that turns out to be is simply the measurements of each side, multiplied.
4 cm x 2 cm x 5 cm gives us 40 cubic cm of space.
So therefore, we say that the volume is 40 cubic cm.
40 of these 1 cubic cm boxes.
And to bring that point home, we can actually count all the boxes. There are 40 cubic cm in that 4 by 2 by 5 cm box.
So for any regular space where you can take the measurement of each dimension, you can use those measurements to figure out the volume.
So let's say you have a cylinder. You measure the cylinder to be 20 cm in height and 2.524 cm in diameter.
If you know how to get the area (the radius, which is half the diameter squared, times 𝞹), in other words 𝞹r², that gives you the area of the cylinder.
And it's 20 cm in height. So when you multiply 𝞹 times the radius squared, giving you the area, times 20 cm, the height, it's going to give you 100 cubic cm.
So if we had the cylinder and it's hollow, and we fill it up with water, the amount of water we could put in it is 100 cubic centimeters.
What if we only filled the water up to 10 cm. Well then we would have 𝞹r², the area, times 10 cm, and that wold give us a total of 50 cubic cm.
And we can do the same with 6 cm. That would give us 30 cubic cm. What if we filled it up to 14 cm?
Well that would give us 70 cubic cm. So in doing this, what we can do is create markings simply by how high the water is to mark the volume for that height of water, or whatever you happen to be filling it with.
And so, these markings are called graduations on the side of a cylinder.
And they tell you the volume of a liquid filled to that mark.
So what we can do here is see how what we call a "graduated cylinder" is made.