00:01
So for this question, we want to find the volume again.
00:05
I'm painting by rotating the region bounded by x equals 2 times the square root of y, x equals 0, and y equals 9, about, rotated about the y -axis.
00:15
So once again, we want to start off by drawing the region.
00:22
So the x equals 0 is just the y -axis line, so we don't really have to care about that.
00:28
The y equals 9, we can just call it like that.
00:34
Now the x equals 2 times the square root of y.
00:39
So typically the square root of y looks like this kind of shape, or this kind of shape.
00:46
But the 2 times the square of y, basically what it does is that it basically makes it wider.
00:53
So it's still the same shape.
00:55
We don't really care about what it specifically looks like because this is just a rough sketch.
01:00
So if we draw across the y equals 9 line, you'll see that this is just a rough sketch.
01:06
This is the region we are rotating about the x -axis, about the y -axis, excuse me.
01:13
So once again, you'll see that we are actually making circles.
01:20
So this brings us to the cross -sectional area function.
01:24
And in this case, it will be in terms of y equals pi r squared, r is equal to two.
01:34
Because in this case, r is equal to the x value...