00:01
We're given a parabola y square equals to 4a x.
00:06
So it will look like this.
00:13
So this will be the parabola.
00:22
Now we want to find the volume of the shape of solid generated by revolving this parabola around the y axis, but it is bounded by its lactose rectum.
00:44
Now, the lattice rectum would be the focal point is here, which is a0.
00:54
The lattice rectum is a line segment that is perpendicular to the axis of symmetry, which is over here.
01:05
This is the axis of symmetry for the graph.
01:15
And this lattice rectum passes through the focus of the parabola.
01:25
And the endpoints of the lattice rectum will end on the parabola.
01:34
And at this point here, this will be a to a and this is a minus 2a.
01:41
So this line segment here is the lattice rectum.
01:48
So we're looking at this shaded region here, being revolved around the y -at -c's forming a solid.
02:00
If i were to just take this line segment here and this shaded region here, the volume of solid will be having the same volume as this portion here.
02:17
So all i need to do is just multiply by two and just need to integrate just this part only.
02:23
So the volume of the real shaped solid generated by revolving about y axis, that would be i'm taking two times.
03:04
Now the volume formula will be pi integrate with respect to y axis because we're revolving around the y axis...