00:01
All right, friends, let's take a look at this problem.
00:02
So what we are looking at here are three situations where we are going to rotate a figure around an axis.
00:09
So our first example here, we are going to be rotating around the y -axis.
00:15
So i'm going to go ahead and write y -axis here.
00:18
And my figure looks like this.
00:21
So this is a two -dimensional figure, just like this.
00:25
And what i'm doing is a two -dimensional solid.
00:27
So i'm going to shade this in.
00:30
And what i want you to think about as you're looking at this is i want you to visualize a pencil that you're holding in front of you.
00:37
And then i want you to visualize taking a post -it note that is in that shape of the figure and rotating that around your pencil vertically.
00:47
And what you're going to see and what you're going to notice is that you have a cone.
00:53
It's going to rotate around just like this and it's going to create a cone, kind of like a hat.
01:00
Kind of like a party hat, if you will.
01:02
So the shape here is going to be a cone.
01:07
The shape is going to be a cone.
01:09
Now, let's take a look at the second one.
01:11
So the second one here, we are also going to rotate around the y -axis.
01:16
And the shape that we are looking at is a semicircle.
01:22
So we're looking at a semicircle.
01:24
And again, our semicircle is a solid.
01:26
So again, if you can visualize in your mind, taking a pencil, and then cutting out a post -it note to be the shape of this semicircle, you can visualize this by spinning that pencil around and looking at the post -it note...