Problem SG 03

Consider a circle of radius 100-feet. Let the circle increase it’s radius by another 10-feet. What is the change in area? We provide two alternative solutions.
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  • Solution 1: A straight forward calculation that subtracts the final area from the initial area.
    • In[]:=
    Pi((100+10)^2-100^2)
    Out[]=
    2100π
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  • Solution 2:
    • In[]:=
    dA=D[Pir^2,r]
    Out[]=
    2πr
    ∴ dA = 2 π r dr
    Substituting values,
    In[]:=
    dA=2*Pi*100*10
    Out[]=
    2000π
    We have a problem that the two answers do not agree. Which is correct?