If a circle with another circle cut out is called a washer, what's the spherical equivalent called?

Question

A circle with a smaller concentric circle cut out of it is called a washer. What would a sphere with a smaller concentric sphere carved out of it be called?

An example is the shape of the first structure in the image below:

By Mariana Ruiz Villarreal ,LadyofHats - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=3032610

Answer 1

Short Answer: The object described in the question is a spherical shell.

Further Discussion:

• A disk with a smaller disk removed is an annulus.

  A washer is a small, flat, usually circular (though other shapes exist) piece of metal with a hole in the middle of it. Washers are a real-world device typically used for spacing—as such, one of the essential properties of a washer is that it has thickness. In elementary calculus classes, students are often taught to find the volume of a solid of rotation using the "washer method". This method approximates the volume of the solid using washer-shaped solids, which are probably better described mathematically as cylinders with annular bases.

  In general, I would probably avoid using the term "washer" in any mathematical context beyond an elementary calculus class. As demonstrated by the original question, the term does not seem to have a clear meaning (the asker uses "washer" as a synonym of "annulus"; I think that many others would understand a washer to be a short cylinder with an annular base). If one insists on using the term, a sentence or two explaining what, precisely, is meant would be helpful.

• In higher dimensions (more general metric spaces), the analog of an annulus is a spherical shell, which is the solid region between two concentric spheres of different radius. Alternatively, a sphereical shell is a ball with a smaller ball (with the same center) removed.

  In a metric space $(X,d)$, a ball is the collection of all of the points within a fixed radius of a specified point (the center). The open ball $B(x,r)$ with radius $r$ and center $x$ is the set $$B(x,r) = \{ y \in X \mid d(x,y) < r \}, $$ and the closed ball $\overline{B}(x,r)$ with radius $r$ and center $x$ is the topological closure of the open ball with the same center and radius. Given two radii $r_1$ and $r_2$ with $r_1 < r_2$, and a fixed point $x$, the spherical shell with inner radius $r_1$, outer radius $r_2$, and center $x$ is the set $$ \overline{B}(x,r_2) \setminus B(x,r_2). $$ In $\mathbb{R}^3$ (three dimensional Euclidean space), this becomes $$ \left\{ y \in \mathbb{R}^3 \mid r_1 \le \|x - y\| \le r_2 \right\}, $$ which is precisely the shape described in the question, above. If $\mathbb{R}^3$ is replaced with $\mathbb{R}^2$, then the definition reduces to the definition of an annulus.

Answer 2

As the comment says, the term is spherical shell:

In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii.