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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

`(4-pi)x=pir`

B

x=2r

C

2x=r

D

`2x=(pi+4)r`

Text Solution

Verified by Experts

The correct Answer is:
2
we have `4x+2pir=2`
Now sum of areas of square and circle is `x^(2)+pir^(2)`
`rarr f(R )=(1-pir)/(2)+pir^(2)`
`rarr (df(r ))/(dr)=2(pir-1)/(2)(pi)/(2)+2pir`
`(df(r ))/(dr)=0`
`rarr r=(1)/(pi+4)`
from `1, 2x=(4)/(pi+4)`
`rarr x=2r`
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