Verify Archimedes’ law for an upright cone of radius R and height H by direct calculation using Eq. (4.3-1). It is convenient to use a combination of Cartesian and spherical coordinates, as shown in Fig. P4.8, and to set P = 0 at z = 0. Note that the side of the cone corresponds to θ = π − β, where β is the cone angle.

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Fp || -fn² ds np S == (4.3-1)