ANSWERS: 2
  • y=(-x^2 + r^2)^(1/2) Should give you your semicircle. (note you should only have positive values for y) Another way to write this formula is x= (-y^2 + r^2)^(1/2) The sides of your rectangle will be 2x and y. The area of your rectangle will be 2x*y you can replace that y with the function of your semicircle, so now your area is.. A= 2x*(-x^2 + r^2)^(1/2) Graph it! Find the max, in terms of (x,y), and the dimensions of the rectangle will be 2x by y. Your answer will depend on your r, but your max area will be on the same part of every sized circle.
  • I recommend that you make a mirror image of the semicircle and the rectangle, flipping about the diameter. Than you will have a rectangle of double area inscribed into a full circle, and the question becomes : what rectangle inscribed into a circle has max area. The answer is the square, due to symmetry (I just restored that symmetry for you). So your initial rectangle inscribed into semicircle was [ r√2 ] x [ r/√2 ]

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