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NEET Sample Paper NEET Sample Test Paper-12

  • 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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