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An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
The volume of a capsule is calculated by adding the volume of a ball of radius (that accounts for the two hemispheres) to the volume of the cylindrical part. Hence, if the cylinder has height h {\displaystyle h} ,
A spherical segment Pair of parallel planes intersecting a sphere forming a spherical segment (i.e., a spherical frustum) Terminology for spherical segments.. In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes.
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.
Consider the linear subspace of the n-dimensional Euclidean space R n that is spanned by a collection of linearly independent vectors , …,. To find the volume element of the subspace, it is useful to know the fact from linear algebra that the volume of the parallelepiped spanned by the is the square root of the determinant of the Gramian matrix of the : (), = ….
The wine gallon, which some sources relate to the volume occupied by eight medieval merchant pounds of wine, was at one time defined as the volume of a cylinder 6 inches deep and 7 inches in diameter, i.e. 6 in × (3 + 1 / 2 in) 2 × π ≈ 230.907 06 cubic inches.
Hart (2009) [3] states that the "volume of a spherical wedge is to the volume of the sphere as the number of degrees in the [angle of the wedge] is to 360". Hence, and through derivation of the spherical wedge volume formula, it can be concluded that, if V s is the volume of the sphere and V w is the volume of a given spherical wedge,