posted by Gul

The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm.

1) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.)

2) What is the relative error? (Round your answer to three decimal places.)

1. Steve

v = 4/3 pi r^3
dv = 4 pi r^2 dr

c = 2pi r
dc = 2pi dr
so, dr = dc/(2pi)
meaning that

dv = 4 pi r^2 dc/(2pi)
= 2 r^2 dr

so, using the given numbers,

dv = 2*(80/2pi)^2 * 0.5 = 1600/pi^2

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