00:01
In this question, we are asked to find the volume of the solid generated by rotating the region bounded by the given lines around the line x equals to negative 1.
00:11
And the first step is to draw the picture of the region and of the solid.
00:29
All right.
00:31
X equals 0 is basically the y -axis.
00:36
Y equals 0 is the x -axis.
00:39
The line y equals to 12 minus 6x.
00:41
When x equals to 0, we are going to get 12.
00:46
Let's say 12 is here.
00:49
And when x equals to...
00:53
When x equals to 2, y equals to 0.
00:58
Let's say x equals 2 is somewhere here.
01:01
So this is a line, y equals to 12 minus 6x.
01:05
This is one boundary of the region.
01:08
Another boundary of the region is y equals 0, which corresponds to the x -axis.
01:12
And the third boundary of the region is x equals 0.
01:15
Which corresponds to the y -axis.
01:18
So this is a region that we are asked to rotate about the line x equals to negative 1.
01:32
And this is a line x equals to negative 1.
01:39
And we are asked to rotate the region about that line.
01:43
And as we are rotating our region around that line, the region sweeps out a solid.
01:54
And we are asked to find the volume of that solid.
02:15
So this is a picture of the solid.
02:18
It will look like kind of a cone, but a hollow cone, right? it's a cone, but there is a hole in that cone.
02:29
It's a hollowed cone...