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[Solved] The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is (x/100)%.

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The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is (x/100)%. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is

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ρ = m/{4/3π(d/2)3}

ρ = 6m/πd3

taking log

ℓnρ = ℓnm - 3ℓnd

Maximum error by differentiation

dρ/ρ = dm/m + 3 dd/d

dρ/ρ = 6 + 3 x 1.5

= 10.5% = 1050/100 %

x = 1050

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