## You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece w

Question

You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum

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1 week 2021-09-15T19:13:13+00:00 1 Answer 0

Therefore the circumference of the circle is

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

For maximum or minimum

Differentiating with respect to r

Again differentiating with respect to r

> 0

For maximum or minimum

Therefore at  , A is minimum.

Therefore the circumference of the circle is