 The last four examples on your note sheet involve using volume of prism, cylinder, pyramid, and cone. If you wanted to try these four on your own and then come back and watch the video, you could do that. Or if you're not sure how to get started, feel free to continue watching. And then maybe pause and try to finish the problem, come back and check your answer. This example you can see has two three-dimensional shapes. It has a prism on the bottom and a pyramid on the top. So in order to find the volume of this shape, we're going to end up taking the volume of the prism and adding the volume of the pyramid. So we're going to start by writing down our volume formulas, which volume of a prism is area of base times the height. The volume of the pyramid is one-third times the area of the base times the height. Now, starting with our prism. Well, hopefully it's pretty obvious that this is a square prism because you see that we have ten by ten. And so the area of that square is ten times ten, and the height of the prism is also given to us, which is fourteen. So no problem there. The problem comes when we go over to the pyramid. Now, the base of the pyramid is the exact same square. So finding the area of the base, that part's easy. Ten times ten. We run into a little glitch when we have to give the height. And that is because they give us the slant height of the pyramid is thirteen. We need the height of the pyramid, which is this. So what I'm going to do is I'm going to draw a right triangle. And I still have a problem because I don't know what that is. So what I'm going to do is I'm going to come down here and I'm going to draw this square. Okay, so what I'm doing is just redrawing this square. And I'm showing you that this piece right here is that. So the reason that that is helpful is because if this is a square that's ten by ten, then I know that this is five and this is five because it's half of the base of the square. So what is that third side then? Well, we have a 4590 triangle. And if the legs are both five, then hopefully you recognize that the hypotenuse is five root two. Which means if we go back to our picture up here, this side of the right triangle has to be five root two. So if I have 13 and five root two, then I will be able to use Pythagorean Theorem to solve for h. So down here I'm going to set up h squared plus five root two squared equals 13 squared. Now, if you are solving for h, notice in the directions that it's approximate. So go ahead and when you're solving for h, just round your answer. h is equal to the square root of 119. And actually I'm not going to round my answer until I plug it back in over here. So I'm going to leave h as the square root of 119 when I put it in to my formula. And then 10 times 10 times 14 is 140. One third times 10 times 10 times square root of 119 is approximately 37. And so when I add those together, I should get about 177 cubic yards for the volume of this shape. Number nine, we have the volume of a right triangular pyramid is 168 cubic units. The right triangle that makes up the base of this pyramid has legs that measure six units and eight units. We want to find the height of the pyramid. So what we're going to do is, because we're dealing with a pyramid, we're doing one third times the area of the base times the height. And because it is a right triangle, the area of the base is one half times the base times the height of the triangle times the height of the pyramid. Now we're going to plug in the volume. They tell us it's 168 and we have that is equal to one third times one half. Now, nice enough, they gave us the legs of this right triangle. So the six and the eight are what you're going to use for the base and the height of that right triangle. And we will be able to solve this for h. If you figure out one third times one half times six times eight, you should get it to equal eight h equals 168. To solve for h, you just divide by eight and we get a height of 21 units.