Calculations at a spherical shell. A spherical shell or hollow sphere is made of two spheres of different sizes and with the same center, where the smaller sphere is subtracted from the larger. Enter at radiuses and at shell thickness two of the three values and choose the number of decimal places. Then click Calculate.
Formulas:
a = R - r
A = 4 * π * ( R² + r² )
V = 4/3 * π * ( R³ - r³ )
pi:
π = 3.141592653589793...
Radiuses and thickness have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit. Surface area refers to inner and outer boundary surfaces.
The surface of a spherical shell refers to the outer and inner surfaces. If only the outer surface is relevant, then this is of course the same as that of a sphere. The symmetry properties are also the same as those of a sphere. The spherical shell is point-symmetrical to the center, which is not part of this geometric body. It is axially symmetrical to any plane through its center and rotationally symmetrical to any angle and in any direction to this center.
Some real things that are spherical are actually spherical shells, simply because there is often no reason to fill the inside of the sphere and you can save material this way. The shell thickness should then of course be chosen so that the object is stable. The earth is of course not hollow inside, but you can imagine its various layers, apart from the inner core, as spherical shells. For example, the outermost layer, the earth's crust, has an outer radius (large sphere) of about 6370 kilometers and is on average about 20 kilometers thick. Of course, this calculation is only approximate, since on the one hand the crust thickness varies greatly, and on the other hand the Earth is actually rather a slightly flattened spheroid.