More Volume Problems : Under this section we are decide to take a look at several more volume problems. Though, the problems we see now will not be solids of revolution while we looked at in the earlier two sections. There are various solids out there which cannot be produced as solids of revolution, or else at least not simply and therefore we require taking a look at how to do several of these problems.

Here, having said that such will not be solids of revolutions they will even be worked in pretty much similar way.  For each solid we will require to find out the cross-sectional region, either A(x) or A(y), and they utilize the formulas we used in the earlier two sections,

The "hard" part of such problems will be finding what the cross-sectional area for all solids is. All problems will differ and therefore each cross-sectional region will be found through various means.

Well before we proceed with any illustrations we require acknowledging that the integrals under this section might look a small tricky at first. There are very few problems.  All of the illustrations into this section are going to be more common derivation of volume formulas for specific solids. For this we'll be working with things as circles of radius r and we will not be providing an exact value of r and we will have heights of h in place of specific heights and so on.

All the letters into the integrals are going to create the integrals look a small tricky, although all you must remember is that the r's and the h's are only letters being used to characterize a fixed quantity for the problem, that is this is a constant. Thus when we integrate we only require worrying about the letter in the differential as i.e. the variable we are really integrate regarding. All other letters in the integral must be thought of as constants. Just think about what you would do if the r was a 2 or the h was a 3 for illustration, if you have trouble doing that.

Let's begin with a simple illustration which we don't really need to do an integral which will exemplify how these problems work in common and will find us used to seeing numerous letters in integrals.