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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Adeline 2 weeks 2021-09-13T13:53:25+00:00 1 Answer 0

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    2021-09-13T13:55:21+00:00

    Answer:

    D(V)  = 100,48 cm³

    Step-by-step explanation:

    The volume of a sphere is:

    V(s) = 4/3 π*r³

    Where r is the radius of the sphere

    If we take derivative of V  respect r

    D(V)/ dr  =  4/3*3*π*r²    ⇒ D(V)/ dr  = 4*π*r²   ⇒ D(V) =  4*π*r²*dr

    We know:

    r = 20 cm     and   dr  =  0,02  ( at most)

    Then

    D(V)  = 4*π*(20)²*0.02  cm³

    D(V)  = 32*π      

    D(V)  = 100,48 cm³

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