Cross Section to the other side

This post is on the concept of the cross section. If you've forgotten your elementary school geometry, this material is for you!

First - the definition: a cross section is the intersection of a plane surface with that of a three-dimensional geometric shape (or alternatively the intersection of a line with a 2-D object).

When you slice a block of cheese, a loaf of bread or even a hot dog, you create a cross section from a geometric shape. For example, here's a cube.

Here's our cube intersected by a reddish plane. The bright red surface is the cross section. With this diagonal cut we get a triangle.

Here's another way you can do a cross section through a cube. This cut gives us a square shape cross section. If we did a cut at a different angle, could we get a rectangle?

I think we can and we have here, but this is about the limit of my 3-D conceptualization and drawing skills. 

Now let's try cutting a section off of a cylinder that's laying on its side. We get a circular shape if we cut at 90% to the main axis of the cylinder. If we cut at an angle, we'd get an oval (ellipse).

Now let's cut up a sphere. Looks like an olive, doesn't it?

After all this virtual practice, I think it's time to go cut up some real food now - it's time for lunch.  

If you want to play with some online cross-sectioning tools, you can go to the Learner.Org website and chop up some geometric shapes.