Question

Describe in words the region of R3 reperesented by the equations or inequalities x2+y2+z2≤3

Answer 1

Answer:

The region represented by the equation is a full sphere of radius √3 centered in the origin of coordinates.

Step-by-step explanation:

In a plane xy, the equation that represents a circle with center in the origin, of radius r is

$x^2+y^2=r^2$

in R³, or a space xyz, we can represent a sphere with its center in the origin, and of radius r, with the equation

$x^2+y^2+z^2=r^2$

So, in this problem we have that

$3=r^2$

which means that the sphere has a radius of √3.

Finally, our equation is an inequality, and the sphere is equal to, and less than, the calculated radius.

Therefore, the sphere is "full" from the surface to its center.