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

• daykie08
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.
daykie08

## 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

## The Attempt at a Solution

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

Last edited:
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

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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

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.

## 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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