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  2. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    where SA is the surface area of a sphere and r is the radius. H = 1 2 π 2 r 4 {\displaystyle H={1 \over 2}\pi ^{2}r^{4}} where H is the hypervolume of a 3-sphere and r is the radius.

  3. On the Sphere and Cylinder - Wikipedia

    en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

    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.

  4. 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 angle, i.e., φ is the angle between the rim of the cap and the direction ...

  5. Spherical segment - Wikipedia

    en.wikipedia.org/wiki/Spherical_segment

    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.

  6. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    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.

  7. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The volume of a sphere with radius r is ⁠ 4 / 3 ⁠ πr 3. The surface area of a sphere with radius r is 4πr 2. Some of the formulae above are special cases of the volume of the n-dimensional ball and the surface area of its boundary, the (n−1)-dimensional sphere, given below. Apart from circles, there are other curves of constant width.

  8. 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,}

  9. 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.