## The radius of a sphere was measured and found to be 20 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error

Question

The radius of a sphere was measured and found to be 20 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

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Math
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2021-09-13T13:53:25+00:00
2021-09-13T13:53:25+00:00 1 Answer
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## Answers ( )

Answer:D(V) = 100,48 cm³Step-by-step explanation:The volume of a sphere is:V(s) = 4/3 π*r³Where r is the radius of the sphereIf we take derivative of V respect rD(V)/ dr = 4/3*3*π*r² ⇒ D(V)/ dr = 4*π*r² ⇒ D(V) = 4*π*r²*drWe know:r = 20 cm and dr = 0,02 ( at most)ThenD(V) = 4*π*(20)²*0.02 cm³D(V) = 32*πD(V) = 100,48 cm³