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A wire of length 28 c m is bent to form a circular sector, then the radius (in cm ) of the circular sector such that the area of the circular sector is maximum is equal to

Options

  1. A5
  2. B6
  3. C7
  4. D8

Correct answer

C. 7

Step-by-step solution

2 r + r θ = 2 8 θ = 28 - 2 r r … 1 Area = A = 1 2 r 2 θ A = 1 2 r 2 28 - 2 r r A = 1 2 28 r - 2 r 2 d A d r = 28 - 4 r 2 = 0 ⇒ r = 7 c m Also, d 2 A d r 2 r = 7 < 0 So, for the area to be maximum, r = 7 c m

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