Posted by Gul on Sunday, March 30, 2014 at 11:17pm.
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.)

Calculus Help Please!!!  Steve, Monday, March 31, 2014 at 12:05am
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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