# Calculus III Question

1. Aug 23, 2007

### omohiuddin

I have a few questions on a problem in my first Calc III class. "The solid cube in the first octant bounded by the coordinate planes and x=2,y=2 and z=2, write the inequality to describe the set". I am new to the 3 dimensional cartesian system, but i still do not get the concept of the octants because i figured their would be 12, 4 for each plane. and also,
x^2 + Y^2 <=1 and no restriction on Z, how does this graph look like. I have been having trouble with those 2 problems. I would greatly apreciate your help.

2. Aug 23, 2007

### symbolipoint

In two dimensions on the cartesian plane, you have four quadrants. When you include the third dimension, you may call the number line the z axis. This z axis points above and below the x y plane; above the x y plane will be four octants and below the x y plane will be another four octants. 4 + 4 = 8.

3. Aug 23, 2007

### nicktacik

4. Aug 24, 2007

### HallsofIvy

Staff Emeritus
But you are not restricted to the coordinate planes. In the xy-plane you have 2 coordinate axes each having 2 sides: they divide the plane into 22= 4 quadrants. In 3 dimensions, you have 3 coordinate axes that divide the entire space into 23= 8 "octants". You can also, as nicktacik said, look at the signs: each of x, y and z can be either positive or negative: again 23= 8 possible combinations

In the plane, $x^2+ y^2\le 1$ is the unit disk. Since z can be anything imagine the disk moving straight up and down: you have the inside of an infinitely long cylinder.