2
$\begingroup$

"A 10-meter length of wire is available for making a circle and a square. How should the wire be distributed between the two shapes to maximize the sum of the enclosed areas?"

Here's what I have: $$Area_c = \pi r^2$$ $$Area_s = 4r^2$$

So, I'm thinking that I need to find the maximized radius size to figure everything else out. $$Area_c + Area_s = 10$$ $$(\pi r^2) + (4r^2) = 10$$

$${\operatorname{d}\over\operatorname{d}r} [(\pi r^2) + (4r^2) - 10] = 2\pi r + 8r$$

But here's my dilemma; if I take the derivative of that and solve for $r$, it comes out 0. So I'm not sure where I'm going wrong. Any advice?

  • 0
    The length of the wire is $10$ meters. Your equation says that the sum of the areas is $10$. The length of the wire is the sum of the perimeters.2011-04-20
  • 0
    I'm a little unsure how to pull this off without another constraint. It seems like a circle is the most efficient shape in terms of containing the most area, so any expression you come up with would force the square's perimeter to zero and give you a circle with circumference = 10 meters.2011-04-20

2 Answers 2