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Volume of a Sphere

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    Volume of a Sphere

    Result

    V = (4 ? a^3)/3 (assuming radius a)

    Example plot

    Example plot

    Equations

    x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = a cos(v)

    x^2 + y^2 + z^2 = a^2

    Surface properties

    2

    g = 0

    S = 4 ? a^2

    ds^2 = a^2 sin^2(v) du^2 + a^2 dv^2

    dA = a^2 sin(v) du dv

    x^_ = (0, 0, 0)

    I = ((2 a^2)/5 | 0 | 0 0 | (2 a^2)/5 | 0 0 | 0 | (2 a^2)/5)

    K(u, v) = 1/a^2

    (for a sphere with center at the origin and radius a)

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