The radius of a sphere was measured and found to be 19 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere?

gladilkamwy

gladilkamwy

Answered question

2022-08-06

The radius of a sphere was measured and found to be 19 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere?
If the radius of the sphere is r then its volume is V = 4 3 π r 3 . If the error in the measured value of r is denoted by d r = Δ r, then the corresponding error in the calculated value of V is Δ V, which can approximated by the differential.

Answer & Explanation

Michelle Chavez

Michelle Chavez

Beginner2022-08-07Added 13 answers

Answer:
V = 4 3 π r 3 d v d r = 3 × 4 π r 2 3 = 4 π r 2 d v = 4 π r 2 d r d v = 4 π r 2 d r r 2 d v = 4 π r r 2 d r = 4 π × 19 × 19 × 0.02 90.68 = 91 = 91 c m 2

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