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COMEDK2016MathematicsApplication of Derivatives

A circular sector of perimeter 60 ~m with maximum area is to be constructed, The radius of the circular arc in metre must be

Options

  1. A10
  2. B15
  3. C5
  4. D20

Correct answer

B. 15

Step-by-step solution

Perimeter of sector =2 r+r 60=2 r+r (given) = 60-2 r r Now, area of sector, (A)= r² 360^ = r²(60-2 r) 360 r aligned &= r 180 (30-r) d A d r &= 180 (30-2 r) aligned For maximum area d A d r =0 aligned & 30-2 r=0 & 2 r=30 r=15 aligned and d² A d r² = 180^ (-2)=- 90 < 0 Hence, it is maximum at r=15 ~m

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