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The volume can be computed without use of the Gamma function. As is proved below using a vector-calculus double integral in polar coordinates, the volume V of an n-ball of radius R can be expressed recursively in terms of the volume of an (n − 2)-ball, via the interleaved recurrence relation:
Some SI units of volume to scale and approximate corresponding mass of water. To ease calculations, a unit of volume is equal to the volume occupied by a unit cube (with a side length of one). Because the volume occupies three dimensions, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m 3).
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.
This equation reduces to that of the volume of a sphere when all three elliptic radii are equal, and to that of an oblate or prolate spheroid when two of them are equal. The volume of an ellipsoid is 2 / 3 the volume of a circumscribed elliptic cylinder , and π / 6 the volume of the circumscribed box.
In Euclidean n-space, an (open) n-ball of radius r and center x is the set of all points of distance less than r from x.A closed n-ball of radius r is the set of all points of distance less than or equal to r away from x.
The freight carrier will measure the longest dimension in each of the three axis (X, Y, Z) and use these measurements to determine the package volume. If the package is a right-angled rectangular box , then this will be equal to the true volume of the package. However, if the package is of any other shape, then the calculation of volume will be ...
A cushion filled with stuffing. In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch.
An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2] V ≈ 4 π r 2 t , {\displaystyle V\approx 4\pi r^{2}t,}