Minimizing Area word problem...Help?

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Minimizing Area word problem...Help?

Postby j0hnx777 on Tue Apr 02, 2013 10:21 am

A 24-in piece of string is cut into two pieces. One piece is used to form a circle wile the other is used to form a square. How should the string be cut so that the sum of the areas is a minimum?

I'm having a hard time setting this one up. Would anyone be willing to help me? Thank you in advance.
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Re: Minimizing Area word problem...Help?

Postby maggiemagnet on Tue Apr 02, 2013 12:26 pm

j0hnx777 wrote:I'm having a hard time setting this one up.

What have you tried? What variable did you start with, etc?

j0hnx777 wrote:A 24-in piece of string is cut into two pieces. One piece is used to form a circle wile the other is used to form a square. How should the string be cut so that the sum of the areas is a minimum?

If one of the cut pieces is length "s", what expression is the other length? (Use what "how much is left" thing they describe here.)

Let's say you use the s-inch piece for the square. Then the sides are s/4, so what is the area? The other piece is for the circle, and the length is the circumference. Plug this into the formula C = 2(pi)r to get r in terms of s. Then plug this into the formula A = (pi)r^2.

Once you have the two areas you can add them and then find the vertex for the minimum. If you get stuck, please write back showing how far you got in doing the steps I've listed. Thanks!
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