The percentage errors in the measurement of mass, diameter and length of a solid cylinder are
2%, 3% and 4% respectively. What will be the maximum percentage error in the estimate of the
density of the material?
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Explanation:
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Given info : The percentage errors in the measure of mass diameter and length of a solid cylinder are 2%, 3% and 4% respectively.
To find : the maximum percentage error in the estimates of the density of the material.
solution : we know, density = mass/volume
⇒D = m/v = m/πd²l/4
therefore, relation of m, r , l and d to find error.
∆D/D = ∆m/m + 2∆d/d + ∆l/l
∴ % error in D = % error in m + 2 × % error in d + 2 % error in l
given, % error in m = 2 %
% error in d = 3 %
% error in l = 4 %
∴ % error in D = 2 % + 2 × 3 % + 4 %
= 2 % + 6 % + 4 %
= 12 %
Therefore the maximum percentage error in the estimate of the density of the material is 12 %.