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NEET AIPMT SOLVED PAPER SCREENING 2008

  • question_answer
    If the error in the measurement of radius of a sphere is. 2%, then the error in the determination of volume of the sphere will be

    A) 4%                         

    B)                        6%

    C) 8%                         

    D)                        2%

    Correct Answer: B

    Solution :

    Volume of a sphere \[=\frac{4}{3}\pi \] (radius)3 or    \[V=\frac{4}{3}\pi {{R}^{3}}\] Taking logarithm on both sides, we have \[\log V=\log \frac{4}{3}\pi +3\log R\] Differentiating, we get \[\frac{\Delta V}{V}=0+\frac{3\Delta R}{R}\] Accordingly, \[\frac{\Delta R}{R}=2%\] Thus,        \[\frac{\Delta V}{V}=3\times 2%=6%\]


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