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MHT CET202019 Oct 2020Evening ShiftMathematicsApplication of DerivativesActual

The maximum volume of a right circular cylinder if the sum of its radius and height is 6 ~m is

Options

  1. A16 m³
  2. B32 m³
  3. C4 m³
  4. D64 m³

Correct answer

B. 32 m³

Step-by-step solution

(A) Let height of cylinder be h and radius be r r + h =6 h =6- r Volume of cylinder V = r ² ~h = r² (6-r)= (6 r²-r³ ) For the maximum volume, dV dr =0 (12 r-3 r² )=0 12 r=3 r² r=4 h=6-4=2 . Volume of cylinder = 4² 2=32 m ³

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