A piece of plexiglass is in the shape of a semicircle with radius 2 m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass.
The circle with radius 2m : x^2 + y^2 = 4
The semicircle: y=sqrt(4 - x^2)
The Area: A = 2xy = 2x(sqrt(4 - x^2))
Find A', simplify, and set 0:
x^2 - 2 = 0, and x = sqrt(2), y = sqrt(2)
Take A'' < 0 to verify maximum area.
Therefore, base length = 2x = 2 sqrt(2) meter
width = y = sqrt(2) meter
area = 4 square meter
Cut sqrt(2) away from the center both +, - x direction, and + y direction!