HOME

TheInfoList



Click Here for Items Related To - Spherical shell
OR:
Spherical shell on:   [Wikipedia]   [Google]   [Amazon]

In
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, a spherical shell (a ball shell) is a generalization of an annulus to three dimensions. It is the region of a
ball A ball is a round object (usually spherical, but sometimes ovoid) with several uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used for s ...
between two
concentric In geometry, two or more objects are said to be ''concentric'' when they share the same center. Any pair of (possibly unalike) objects with well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyh ...
sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
s of differing radii.


Volume

The
volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
of a spherical shell is the difference between the enclosed volume of the outer sphere and the enclosed volume of the inner sphere: : \begin V &= \tfrac43\pi R^3 - \tfrac43\pi r^3 \\ mu &= \tfrac43\pi \bigl(R^3 - r^3\bigr) \\ mu &= \tfrac43\pi (R-r)\bigl(R^2 + Rr + r^2\bigr) \end where is the radius of the inner sphere and is the radius of the outer sphere.


Approximation

An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness of the shell: : V \approx 4 \pi r^2 t, when is very small compared to (t \ll r). The total surface area of the spherical shell is 4 \pi r^2.


See also

* Spherical pressure vessel *
Ball A ball is a round object (usually spherical, but sometimes ovoid) with several uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used for s ...
* Solid torus * Bubble *
Sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
* Focaloid


References

{{DEFAULTSORT:Spherical Shell Elementary geometry Geometric shapes Spherical geometry Euclidean solid geometry