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Math Gaviriel
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A wire of length 20 cm is to be cut into two pieces. One of the pieces is to be made intoa square and other into a circle. Where should the wire be cut so that the combined areais minimum ? ​

answers: 1
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Answer:

Answer:

Let one part be of length x, then the other part will be 28−x.

Let the part of the length x be covered into a circle of radius.

2πr=x

⇒r=

x

Area of circle =πr

2

=π(

x

)

2

=

x

2

Now second part of length 280−x is covered into a square.

Side of a square =

4

28−x

Area of square =[

4

28−x

]

2

Thus total area =

x

2

+[

4

28−x

]

2

dx

dA

=

2x

+

16

2

(28−x)(−1)

=

x

8

28−x

Lets take

dx

dA

=0

Thus

x

8

28−x

=0 ....(1)

4x=28π−πx

4x+πx=28π

x[4+π]=28π

x=

4+π

28π

Other part =28−x=28−

4+π

28π

=

4+π

112+28π−28π

=

4+π

112

Now again differentiating, we get

dx

2

d

2

A

=

1

+

8

1

=+ve

A is minimum.

When x=

4+π

28π

and 28−x=

4+π

112

244
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