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All right. So, let's continue with um volume problem with cross-section. So, last time we emphasizing on the cross-section with um circle.

Well, yeah, it's a circle, but we call that um this method. Okay, cuz the cross-section is a circle. And we also have another one circle related we call that washer.

In fact the cross section is a ring. Okay. And this is a circle and those are generated.

So solid generated by rotation. Okay. So this time we're going to look at another type more general like this.

So the cross-section could be for example square could be triangle or circle. Well more precisely semicircle then of course you need to know the formulas right? So the area will be uh side time side for squares.

For triangle, well it has to be special. Well, for triangle, of course, it's 1/2 base times height. But for special ones, well, let me take this down.

For special ones or some other formulas, it could be um 12 a * b * sin theta where theta is the angle between s a and b. Okay. Now, the semicircle of course is 12 pi r².

Okay. And it could be quarter. For example, we could have um quarter like quarter circle and this will be 1/4 * r².

Okay. So those are some possible possible cross-sections. Now to do to to do so solve this prime problems you will see that we have graphs and of course graph is important right so we have to solve it most of the time this is difficult difficult to sketch so normally we don't quite need to sketch this now the base is important must sketch and a cross-section.

Okay, you must sketch because only if you sketch them and then you draw connection as what we um as what we did before. Okay. So what is the connection?

This is the connection. Okay. So that's connection.

Okay. So after this I'm going to demonstrate you know this kind of method um in the following videos.