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AP EAMCET20227 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

If an open cylinder of given surface area has maximum volume, then its radius is

Options

  1. AHeight of the cylinder
  2. BHeight of the cylinder/2
  3. C2 times height of the cylinder
  4. D3 times height of the cylinder

Correct answer

A. Height of the cylinder

Step-by-step solution

Cylinder is open, radius of base =R , height =H Surface area A=2 R H+ R^2 aligned & H= A- R^2 2 R & V= R^2 H= R^2 ( A- R^2 2 R )= R 2 (A- R^2 ) & d v d R = A 2 - 3 R^2 2 =0 A=3 R^2 & d^2 V d R^2 =-3 R < 0 & at A=3 R^2, maximum volume & A=3 R^2=2 R H+ R^2 & R=H aligned

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