A piece of wire 9 m long is cut into two pieces. one piece is bent into the shape of a circle of radius r and the other is bent into a square of side s. how should the wire be cut so that the total area enclosed is:

I have found the minimum r=.6301115 and s=1.26022. I need help finding the maximum radius. Thanks!

To find the maximum radius, we can use the given equation for the total length of the wire:

9 = 2πr + 4s

This equation represents that the sum of the circumference of the circle (2πr) and the perimeter of the square (4s) should be equal to the total length of the wire.

Since we are trying to maximize the radius, we can rearrange the equation to solve for r:

2πr = 9 - 4s
r = (9 - 4s) / (2π)

Now we have an equation to find the radius in terms of the side length of the square (s).

You have already found the minimum values for r and s, so let's substitute those values into the equation to find the maximum radius.

r = (9 - 4(1.26022)) / (2π)
r ≈ (9 - 5.04088) / (2π)
r ≈ 3.95912 / (2π)

To find the maximum radius, you can divide 3.95912 by 2π:

r ≈ 3.95912 / (2π)
r ≈ 0.630115

Therefore, the maximum radius for the given wire length is approximately 0.630115 units.