Questions from practice tests

DrSteve
Mon, 15 Aug 2011 17:10:20 +0000

Here’s another way to think about number 1.

If you look at the usual xy-plane, and draw a circle centered at the origin, you can see that it is split into 4 pieces. This is because there are 4 quadrants.

Now generalize this in 3 dimensions to an xyz-plane. This has 8 octants. Thus if you center a sphere at the origin in the xyz-plane it will be split into 8 congruent pieces.

(The 3 “cuts” are the xy-plane, the xz-plane, and the yz-plane)