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A wire of length 2 units is cut into two...

A wire of length 2 units is cut into two parts which are bent respectively to from a square ofside c units and a circle of radius r units if the sum of the sum of the areas of the square and the circle so fromed is minimum then

A

`2x =( pi + 4) r`

B

`(4-pi)x = pi r`

C

`x = 2r`

D

`2x = r`

Text Solution

Verified by Experts

The correct Answer is:
C
`4x +2pi r 2," "x^2 + pir^2= `minimum
`So f(r) =((1-pi r )/2)^2 + pi r^2 rArr (df)/(dr) = pi^2 r/2 - pi/2 + 2 pi r = 0`
`rArr r = 1/ (pi + 4) ` and ` x = 2r`
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