How Should Wire Be Cut to Minimize Combined Area of Circle and Square?

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In summary, to find the optimal cut for a piece of wire 10ft long, one piece should be bent into a circle with a radius of 5/(pi+4) while the other should be bent into a square with a side of 10/(pi+4). This will result in the combined area of the two figures being as small as possible. To solve this, one must write down the equations for the area of a circle and square, find the connection between the parameters, create a sum of the areas, and differentiate with respect to one variable, setting it equal to zero.
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Homework Statement



A piece of wire 10ft long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of a square. How should the wire be cut so that the combined area of the two figures is as small as possible

Homework Equations


The Attempt at a Solution


radius=r and side of the square=s
answer: r = 5/(pi+4) and s =10/(pi+4)

I have the answer but I don't know how should I do it... Please help
 
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A piece of wire 10ft long is cut into two pieces. One piece is bent ito the shape of a circle and the other into the shape of a square. How should the wire be cut so that the combined area of the two figures is as small as possible

should that be
A piece of wire 10ft long is to be cut into two pieces. One piece is bent ito the shape of a circle and the other into the shape of a square. How should the wire be cut so that the combined area of the two figures is as small as possible
 
  • #3
Write down the equations for the area of a circle and the area of a square. The area of the circle has the parameter r (the radius) and the area of the square has the parameter s (the side of the square). Find the connection between these parameters and between the parameters a and b which represent the two cut pieces of the wire. Further on, create a sum A(a, b) = A1(a) + A2(b). Then plug in the relation between a and b (i.e. a + b = 10). Then you'll get the total area in a single variable, A(a) = ... (or A(b), doesn't matter). Differentiate with respect to that variable and set equal to zero.
 

Related to How Should Wire Be Cut to Minimize Combined Area of Circle and Square?

What is the wire problem?

The wire problem refers to a situation where there is a difficulty or issue with the wiring of a system or device.

Why is the wire problem important?

The wire problem is important because it can lead to malfunctioning or even dangerous situations if not addressed properly.

What causes wire problems?

Wire problems can be caused by various factors such as faulty installation, wear and tear, or damage from external factors.

How can I identify a wire problem?

Some common signs of a wire problem include flickering lights, frequent tripping of circuit breakers, and burning smells. A professional electrician can also perform tests to identify the issue.

What should I do if I encounter a wire problem?

If you encounter a wire problem, it is important to seek help from a licensed electrician. Attempting to fix the issue yourself can be dangerous and may worsen the problem.

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