Steve likes to entertain friends at parties with "wire tricks". Suppose he takes a piece of wire 60 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square.

Where should Steve cut the wire so that the total area of the circle and square combined is as small as possible? What is this minimal area?

What should Steve do if he wants the combined area to be as large as possible?

Question

Steve likes to entertain friends at parties with "wire tricks". Suppose he takes a piece of wire 60 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square. 

 Where should Steve cut the wire so that the total area of the circle and square combined is as small as possible? What is this minimal area? 

 What should Steve do if he wants the combined area to be as large as possible?

anonymous · Answer

ugh someone please help me this is a really important question I need to understand (the wire does need to be cut, it can't just be a circle and no square or vice versa)

anonymous · Answer

Minimum area when the wire is cut into two parts one of length $$\frac{ 60\pi }{ \pi+4 }$$ to make circle and another of length $$\frac{ 240 }{ \pi+4 }$$ to make a square

wolf1728 · Answer

And that is roughly 26.39	for the circle and 33.61for the square.

wolf1728 · Answer

You said the wire has to be cut (not sure if this is for the maximum too).
Anyway, you'll get the maximum total area with 60 inches for the circle and nothing for the square.