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  2. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    where V is the volume of a sphere and r is the radius. S A = 4 π r 2 {\displaystyle SA=4\pi r^{2}} where SA is the surface area of a sphere and r is the radius.

  3. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    Particular care must be taken to check the meaning of the symbols. The mathematics convention. Spherical coordinates (r, θ, φ) as typically used: radial distance r, azimuthal angle θ, and polar angle φ. + The meanings of θ and φ have been swapped—compared to the physics convention. The 'south'-direction x-axis is depicted but the 'north ...

  4. 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,}

  5. Spherical trigonometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_trigonometry

    The sphere has a radius of 1, and so the side lengths and lower case angles are equivalent (see arc length). The angle A (respectively, B and C) may be regarded either as the angle between the two planes that intersect the sphere at the vertex A, or, equivalently, as the angle between the tangents of the great circle arcs where they meet at the ...

  6. Vector fields in cylindrical and spherical coordinates

    en.wikipedia.org/wiki/Vector_fields_in...

    The symbol ρ is often used instead of r. Note: This page uses common physics notation for spherical coordinates, in which θ {\displaystyle \theta } is the angle between the z axis and the radius vector connecting the origin to the point in question, while ϕ {\displaystyle \phi } is the angle between the projection of the radius vector onto ...

  7. 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.

  8. Volume element - Wikipedia

    en.wikipedia.org/wiki/Volume_element

    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 : (), = ….

  9. 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.

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