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

A wire of the 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

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 + pi r^2 `= minimum
`rArr ` So `f(r) = ((1-pir)/(2))^2 + pi r^2 implies (df)/(dr) = pi^2 r/2 - pi/2 + 2pir =0`
`rArr r= 1/(pi+4) and x= 2r`
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