The height of a cylinder is equal to the radius. If an error of a% is made in the height, then percentage error in its volume, is

The height of a cylinder is equal to the radius. If an error of a% is made in the height, then percentage error in its volume, is

  1. A

    a%

  2. B

    2a%

  3. C

    3a%

  4. D

    none of these

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    Solution:

    Let h be the height of the cylinder. Then, its
    volume V is given by

    V=πh3                                                                        [r=h]dVdh=3πh2 ΔV=dVdhΔh ΔV=3πh2Δh ΔVV×100=3πh2πh3Δh×100=3Δhh×100=3α 

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