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  2. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    The volume of a spherical cap with a curved base can be calculated by considering two spheres with radii and , separated by some distance , and for which their surfaces intersect at =. That is, the curvature of the base comes from sphere 2.

  3. Spherical sector - Wikipedia

    en.wikipedia.org/wiki/Spherical_sector

    If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =. This may also be written as V = 2 π r 3 3 ( 1 − cos ⁡ φ ) , {\displaystyle V={\frac {2\pi r^{3}}{3}}(1-\cos \varphi )\,,} where φ is half the cone aperture angle, i.e., φ is the angle between the rim of the cap and the ...

  4. Volume of an n-ball - Wikipedia

    en.wikipedia.org/wiki/Volume_of_an_n-ball

    where S n − 1 (r) is an (n − 1)-sphere of radius r (being the surface of an n-ball of radius r) and dA is the area element (equivalently, the (n − 1)-dimensional volume element). The surface area of the sphere satisfies a proportionality equation similar to the one for the volume of a ball: If A n − 1 ( r ) is the surface area of an ( n ...

  5. Spherical wedge - Wikipedia

    en.wikipedia.org/wiki/Spherical_wedge

    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,

  6. Sphere - Wikipedia

    en.wikipedia.org/wiki/Sphere

    For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of the cube, since V = ⁠ π / 6 ⁠ d 3, where d is the diameter of the sphere and also the length of a side of the cube and ⁠ π / 6 ⁠ ≈ 0.5236.

  7. Surface-area-to-volume ratio - Wikipedia

    en.wikipedia.org/wiki/Surface-area-to-volume_ratio

    Plot of the surface-area:volume ratio (SA:V) for a 3-dimensional ball, showing the ratio decline inversely as the radius of the ball increases. A solid sphere or ball is a three-dimensional object, being the solid figure bounded by a sphere. (In geometry, the term sphere properly refers only to the surface, so a sphere thus lacks volume in this ...

  8. Equivalent spherical diameter - Wikipedia

    en.wikipedia.org/wiki/Equivalent_spherical_diameter

    In this case, the cross-sectional area becomes nearly the same as that of a sphere with equal volume. [6] In addition, the favored mean particle size for laser diffraction results is the D[4,3] or De Brouckere mean diameter, which is typically applied to measurement techniques where the measured signal is proportional to the volume of the ...

  9. Spherical shell - Wikipedia

    en.wikipedia.org/wiki/Spherical_shell

    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,}