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The combined perimeter of a circle and a square is 16m.  Find the dimensions of the circle and the square that produce a maximum total area.  Your solution should be neat, detailed, and organized in a logical manner.

 Oct 30, 2020
 #1
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Hint: the area of the square should be as large as possible.

 Oct 30, 2020
 #2
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I think it is the opposite guest... IDK the best way to explain it, but look at this graph:

 

https://www.desmos.com/calculator/din2ukxbds

 

We wish to find the max value of A while keeping S and R positive.

That appears to occur when  S = 0  and  R = 8/pi

hectictar  Oct 30, 2020
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How would I find the maximum if the graph is opening upwards?

ElitBabbi  Oct 30, 2020
 #4
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You are right!  If a circumference is 16, the area of a circle is 20.372 units squared; the area of a square with a perimeter of 16 is only 16 units squared. 

Guest Oct 30, 2020

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