Description
The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm.
(a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.)
?
What is the relative error? (Round your answer to three decimal places.)
What is the relative error? (Round your answer to three decimal places.)
?
(b) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.)
(b) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.)
?
What is the relative error? (Round your answer to three decimal places.)
What is the relative error? (Round your answer to three decimal places.)
?
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Explanation & Answer
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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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