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MHT CET20225 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

A circular sector of perimeter 60 meter with maximum area is to be constructed. The radius of the circular are in meter must be

Options

  1. A5 ~m
  2. B15 ~m
  3. C10 ~m
  4. D20 ~m

Correct answer

B. 15 ~m

Step-by-step solution

Perimeter =2 r+r =60 = 60-2 r r Area = A ( r )= r ^2 360 = r ^2 ( 60-2 r r ) 360 = 360 (60 r-2 r ^2 )A^ (r)= 360 (60-4 r) For area to be maximum A^ (r)=0 r=15

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