The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm.

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S = 4*pi*r^2

delta S = 8*pi*r delta r = 8*pi*76*0.5 = 955 cm^2

relative error = dela S/S = 8 pi*r*deltar / (4*pi*r^2) = 2delta r/r = 1/76 = 0.013

b) V= 4/3 pi*r^3

dV = 4pir^2 dr = 4*pi*76^2 *0.5 = 36292

relative error = 4pi r^2 dr / (4/3*pir^3) = 3dr/r = 1.5/76 = 0.020

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