If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius λ %, then the error in its volume, is

If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius λ %, then the error in its volume, is

  1. A

    λ %

  2. B

    2λ %

  3. C

    3λ %

  4. D

    none of these

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    Solution:

    let r be the base radius and h be the height of the

    cone. Then, 2r=h. Let V be the volume of the cone. Then,

    V=13πr2h=4πr33dVdr=4πr2ΔV=dVdrΔrΔV=4πr2ΔrΔVV×100=4πr24πr3×100=3Δrr×100=3λ

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