What is the error propagated in the computation of the volume of a sphere with a

Question

What is the error propagated in the computation of the volume of a sphere with a radius of: r=1.00 ± .01 cm?
Express the result as the relative uncertainty (ratio of uncertainty to volume). The volume of a sphere is given by the expression:

What is the error propagated in the computation of the volume of a sphere with a radius of: r=1.00 ± 01 cm? Express the result as the relative uncertainty (ratio of uncertainty to volume). The volume of a sphere is given by the expression: 4 a. Applicable error propagation equation from Appendix 1 of Uncertainty & Error Analysis b. Apply the volume equation to the equation of part (a) to obtain the formula for calculating the volume uncertainty u¡V) as a function of the uncertainty of the radius ufrt. c. Use the value of the radius (r=1.00 ± .01 cm) and the equation of part (b) to compute the value of the volume uncertainty un. d. Express your results in the form: V ± u(V). For example: 12.23 ±.01 Express V and ufV) with the same number of decimal places.

Explanation / Answer

r = 1.00 ± .01 cm

V = Volume = 4 pi r3/3 = 4 (3.14) (1)3/3 = 4.2

deltaV/V = ± 3 deltar/r

deltaV/4.2 = ± 3 (0.01)/1

deltaV = ± 0.126

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