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

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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

TestHub · Accepted Answer

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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