physics

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What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 0.84 ± 0.04m ?

  • physics -

    v = (4/3) pi r^3

    dv/dr = 4 pi r^2
    (which is the surface area of course :)

    dv = 4 pi r^2 dr
    dv/v = 4 pi r^2 dr/(4/3)pir^3

    dv/v = 3 dr/r
    here dr = .04
    and r = .84
    so 100 * 3 dr/r = 12/.84 = 14.3 %

  • physics -

    how do u get dv/v = 3 dr/r ?

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