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
[tex]x^2+y^2=r^2[/tex]
in R³, or a space xyz, we can represent a sphere with its center in the origin, and of radius r, with the equation
[tex]x^2+y^2+z^2=r^2[/tex]
So, in this problem we have that
[tex]3=r^2[/tex]
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.
The region is a sphere of radius √3 with the center at the origin.
As we know that the equation of a sphere is given as,
[tex](x+a)^2 + (y+b)^2+(z+c)^2 = (r)^2[/tex],
where,
(a, b, c) is the coordinate of the center of the sphere,
and r is the radius of the sphere.
[tex]x^2 + y^2+z^2 = r^2[/tex]
Comparing the above equation to the equation of a sphere,
we get that (a, b, c) = (0, 0, 0) and radius r≤√3
therefore, the center of this sphere is at the origin, and the region that will be covered will be inside this sphere of radius √3.
hence, the region is a sphere of radius √3 with the center at the origin.
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