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JEE Main2016MathematicsApplication of DerivativesActual

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then

Options

  1. Ax = 2 r
  2. B2 x = r
  3. C2 x = π + 4 r
  4. D4 - π x = π r

Correct answer

A. x = 2 r

Step-by-step solution

Given that 4 x + 2 π r = 2 i.e., 2 x + π r = 1 ∴ r = 1 - 2 x π .......(i) Area A = x 2 + π r 2 = x 2 + 1 π   2 x - 1 2 For min vale of area A d A d x = 0 gives x = 2 π + 4 .......(ii) From (i) and (ii) r = 1 π + 4 .......(iii) ∴ x = 2 r

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