Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    There is an error of\[\pm 0.04\,\,cm\]in the measurement of the diameter of a sphere. When the radius is\[10\,\,cm\], the percentage error in the volume of the sphere is

    A) \[\pm 1.2\]                        

    B) \[\pm 1.0\]

    C) \[\pm 0.8\]                        

    D)        \[\pm 0.6\]

    Correct Answer: D

    Solution :

    Given, error in diameter\[=\pm 0.04\] Error in radius,\[dr=\pm 0.02\] \[\therefore \]Per cent error in the volume of sphere                 \[=\frac{dV}{V}\times 100=\frac{d\left( \frac{4}{3}\pi {{r}^{3}} \right)}{\frac{4}{3}\pi {{r}^{3}}}\times 100\]                 \[=\frac{3dr}{r}\times 100\]                 \[=\frac{3\times (\pm 0.02)}{10}\times 100=\pm 0.6\]


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