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AP EAMCET202123 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

If the area of a circular sector of perimeter 60 ~m is to be maximized, then its radius must be......... m

Options

  1. A20
  2. B15
  3. C10
  4. D5

Correct answer

B. 15

Step-by-step solution

Given, the perimeter of circular sector =60 ~m Let radius be r ~m . Length of arc A B =l aligned perimeter (p) & =l+2 r l & =p-2 r aligned aligned & Area = 1 2 l r & A= (p-2 r) r 2 = p r-2 r^2 2 aligned For A to be maximum, d A d r =0 d d r ( p r-2 r^2 2 )=0 array rlrl & & p-4 r 2 & =0 & p & =4 r array 60=4 r r=15 ~m

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