# Chapter 12 - Section 12.1 - Three-Dimensional Coordinate Systems - 12.1 Exercises: 35

A "hollow sphere" whose center is hollow when $r<1$ and contains all points (i.e. "thickness") between $1\leq r\leq\sqrt 5$ (center (0,0,0)).

#### Work Step by Step

Start with the formula of a sphere: $x^2+y^2+z^2 = r^2$ We have a maximum r-value of $\sqrt 5$ and a minimum r-value of $1$. Think of $1 \leq x^2+y^2+z^2 \leq 5$ as two spheres: $x^2+y^2+z^2 \leq 5$ and $x^2+y^2+z^2 \geq 1$ The points that are valuable to us are the ones that would be contained on and between these two spheres, $1\leq r\leq\sqrt 5$. That leaves us with a hollow core around the center when $r<1$.

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