Graphs of solids of revolution

[mech-eng]

Is drawing of graphs of solids of revolutions important topic of mathematics? This makes me remerber conic sections topic. Conic sections topic belongs to algebra and drawing their graphs is important. So where does solids of revolutions belong to? I know calculation of their volumes belongs to integral calculus but my question is little different.

Thank you.

 

[Mark44]

Is drawing of graphs of solids of revolutions important topic of mathematics? This makes me remerber conic sections topic. Conic sections topic belongs to algebra and drawing their graphs is important. So where does solids of revolutions belong to? I know calculation of their volumes belongs to integral calculus but my question is little different.

IMO, the graphs of solids of revolution isn't very important on its own. Most of the solids you get don't have their own names like the various conic sections do. As you note, the graphs of solids of revolution are used in the part of integral calculus that deals with volumes of various solids.

That said, if you don't know how to sketch a graph of a solid of revolution, you will have a hard time with the part of calculus that deals with these solids. And when you're working with double integrals, it is very important to be able to sketch a graph of the region over which integration is being done, as well as being able to sketch the solid whose volume the integral represents.

 

[Nidum]

 

[Nidum]

An in depth understanding of how to work with solids of revolution is essential in many areas of engineering design work .

 

[mech-eng]

View attachment 195308

Would you explain how you can do this?
Thank you.

 

[Nidum]

It was done with one of the standard functions available in most 3D CAD systems .

Starts off as 2D drawing of the cross sectional shape required and a line showing where you want the central axis to be . The CAD system then sweeps the shape around to make the solid of revolution .

This is a very simple example . Many other 3D shape generating functions are available .

 

[Mark44]

View attachment 195579 It was done with one of the standard functions available in most 3D CAD systems .

Starts off as 2D drawing of the cross sectional shape required and a line showing where you want the central axis to be . The CAD system then sweeps the shape around to make the solid of revolution .

This is a very simple example . Many other 3D shape generating functions are available .

But can you do it on a grid that with a semilog scale?

 

[symbolipoint]

Would you explain how you can do this?
Thank you.

With or without modern technology?
If without modern technology, how to make sketches of three-D solids is what your Calculus 2 & 3 professor should be showing your class. Hard to explain just using language in text. You need to draw three axes for the three dimensions, done on the 2-D writing surface.