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MHT CET202122 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

The slant height of a right circular cone is 3 ~cm . The height of the cone for maximum volume is

Options

  1. A5 ~cm
  2. B5 ~cm
  3. C3 ~cm
  4. D3 ~cm

Correct answer

D. 3 ~cm

Step-by-step solution

Volume of cone = 1 3 r ^2 ~h We have slant height =3 ~cm and we know that ^2= r ^2+ h ^2 aligned & 9= r ^2+ h ^2 r ^2=9- h ^2 & v = 1 3 (9- h ^2 ) h =(3 ) h - ( 3 ) h ^3 & dv dh =3 - ( 3 ) (3 ~h ^2 )=3 - h ^2 aligned When dv dh =0 , we get 3 = h ^2 h = 3 d ^2 v dh ^2 =0-2 h ( d ^2 v dh ^2 )_ b - 3 =-2 3 < 0 Volume of cone is maximum when h = 3

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