Vertical, angled and horizontal cross sections.

Question

Miguel has a globe on his shelf.  Draw and describe the shape resulting from vertical, angled, and horizontal cross sections of the globe.

 

 

Answer 1

So Conny,

The globe is a ball (sphere). Imagine a sphere in front of you (or, better yet, go make one out of wheat flour and water, firm but can be rolled into shape). Cut it (mentally, or physically) and look at the exposed surface. Are the shapes of the cut surface (probably, your course is only considering the perimeter shape of the exposed surface) different, depending on whether the cut was aligned vertically, horizontally, or otherwise? What is the ONLY shape you can get by cutting a sphere?

Related question: to get from one place to another on the surface of a globe, there is only one shortest path travelling on the surface (called a great circle)(except, if you're going to the exact other end of the globe, then you have choices). How does that shortest path relate to a slice through the globe: what three points must the plane you slice on contain?

Hope this sets you to thinking. P.S.: store the dough ball in your 'fridge, you may need it soon for shapes of sections through cones!

-- S.