 In this video we're going to talk about volume of prisms and cylinders. So what we see in front of you here is a cylinder and a prism. This happens to be a pentagonal prism because the base is a pentagon. And we want to first talk about, before we talk about the actual volume formula, we want to talk about the height of a prism or a cylinder. So when you're talking about the height of a prism or a cylinder, you're always talking about the distance between the two bases. So distance between the two bases. So when I look at these two pictures, I can see that the cylinder has two circle bases here and here. So when I identify the height, it's going to be this distance between the bases. So from the measurement from top to bottom in this case. But remember if the cylinder is on its side, then you can keep in mind that the height is just the distance between the two bases. Same thing for a prism. The height is going to be the distance between the two bases. So in this picture, this right here would be what we call the height. And I use a capital H for that. So to find the volume of a prism or a cylinder, the formula is that you're going to take the area of the base. So I use a capital B because the base can be different shapes. If you're taking a cylinder, it's a circle. In a prism, it could be anything. Really, it could be any shape. It could be a triangular prism or rectangular prism. This one's a pentagonal prism. So I use a capital B for area of the base times the height of the prism. So if you want to write out that that is the area of the base times the height of either the prism or the cylinder. So it just depends on which three-dimensional shape you are working with. So as we move through your note sheet, this first example is showing you how the volume comes together for a right triangular prism. So number one, it says shade in the bases. So hopefully you recognize that the right triangles are the bases of this prism. Label the height of the prism as H. And so remember that the height is the distance between the two bases. So seven would be the height. If we move on to numbers three and four. It actually wants us to calculate the area of the base. So here we have the area of the base, which because it's a triangle, it's going to be one-half times the base times the height. And the base of this triangle is twelve. So one-half times twelve. And the height of the triangle is five. So times five. And if you multiply, you get thirty square units. Now the height of the prism is seven. So remember that we said earlier that the height of the prism is seven. So to calculate the volume, the volume is equal to the area of the base times the height of the prism. Well in this case, the area of the base is a triangle. So one-half times base times height times the height of the prism. Well we already calculated up here that the area of the triangle is thirty. And we know that the height is seven. So when we plug that in, thirty times seven is equal to two hundred and ten. Now really important to know that when you do volume, you're no longer working with square units. You are now working with cubic units. So when I label this, I want to use a power of three on my label. When we talk about volume, we're talking about what it would take to basically fill this shape with, let's just say, liquid. If we were going to fill this with water, it would fill two hundred and ten cubic units. Here we're looking at an example of a cylinder. So label the bases on the cylinder. The bases are going to be the circles. So the top circle and the bottom circle, those are the bases. And because the base is a circle, we know that the area is pi r squared. And by looking at this picture, we can see that the radius of the circle is three. So pi times three squared is nine pi. Notice that it wants exact, so I'm just going to leave it as nine pi. The height of this cylinder is five. So to calculate the volume, which is area of the base times the height of the cylinder, in this case, we're going to do pi r squared times the height of the cylinder. We calculated up above that the area of the circle is nine pi and the height is five. So we would say that this cylinder has a volume of 45 pi. And again, when we label, we would use cubic units. So we put a little three. When we do area it's square units. When we do volume it is cubic units.