00:01
So the tricky thing with this problem, i think, is coming up with the equation.
00:07
But if we have x equals theory, we just think about revolving it around the y -axis like this.
00:15
I least that's how i would approach the problem.
00:18
And then we also have it's six meters high.
00:23
Don't really care about the units, but that's important.
00:26
So i'm just thinking about if i revolve this cone around.
00:32
I don't know if you can even see the cone i'm talking about, removing all this red space in between, that could be the equation, just y equals, i believe it's 2x, like up 6, right, 3 is the same, you know, 6 over 3 for the slope reduces to 2.
00:52
So i think what they want you to do in the problem is think about doing horizontal cross -sections and revolving it that way.
01:03
So let's do that.
01:05
It'd be pi from 0 to 6.
01:08
The upper function, the function that's further away, is x equals 3 squared.
01:14
And then you subtract off the function that's closer, but you have to solve for x.
01:18
So that's the 1 half y that piece needs to be squared, dy.
01:26
So i think we can do all these steps at once because 3 squared is 9, so it's integral to be 9 y.
01:32
Just make sure you square each one of those pieces.
01:35
So it's really one fourth...