If the radius of a sphere is 50+-1....show that the uncertainty of its

1.	If the radius of a sphere is 50+-1....show that the uncertainty of its volume is 6%
Answer» Answer: V = 4/3 pi R^3 dV = 4 pi R^2 differential of V dV / V = 3 dR / R = 3 * 1 / 50 = .06 = 6% That assumes you have had calculus If not then you need to EXPAND (R + dR)^3 and drop terms that CONTAIN dR^2 and dR^3 because they are small that is [(R + dR)^3 - R^3] / R^3

If the radius of a sphere is 50+-1....show that the uncertainty of its volume is 6%

Answer»

Answer:

V = 4/3 pi R^3

dV = 4 pi R^2 differential of V

dV / V = 3 dR / R = 3 * 1 / 50 = .06 = 6%

That assumes you have had calculus

If not then you need to EXPAND (R + dR)^3 and

drop terms that CONTAIN dR^2 and dR^3 because they are small

that is [(R + dR)^3 - R^3] / R^3

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If the radius of a sphere is 50+-1....show that the uncertainty of its volume is 6%

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