Answer:
[tex]r^2<x^2 + y^2+z^2 < R^2[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]r < R[/tex]
where r and r are the radius of the circle.
General equation of circle:
[tex](x-h)^2 + (y-k)^2 + (z-j)^2 = r^2[/tex]
where(h,k,j) is the center of the circle and r is the radius of circle.
If the circle is centered at origin, then,
[tex]x^2 + y^2+z^2 = r^2[/tex]
Equation of circle with radius R centered on origin
[tex]x^2 + y^2+z^2 = R^2[/tex]
Inequality to describe the region that consist of all points lying between the sphere of radius r and R but not on the sphere is given by:
[tex]r^2<x^2 + y^2+z^2 < R^2[/tex]
