Question

Describe the sets of points in space whose coordinates satisfy the given inequalities or combinations of equation and inequalities.
$1\le x^2+y^2+z^2\le 4$

Answer 1

Since,

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

denotes sphere with center at $(0,0,0)$ and radius$=a$

So, the region denoted by

$1\le x^2+y^2+z^2\le 4$

will be a shell (hollow) whose inner radius$=1$ and outer radius $=2$