Reducing waste
What is less wasteful: to cut out a circle from a square, or a square from a circle?
Problem source: MathsChallenge.net.
What is less wasteful: to cut out a circle from a square, or a square from a circle?
Problem source: MathsChallenge.net.
February 19th, 2010 at 2:05 am
Cutting a circle from a square:
The least wasteful (i.e. largest) circle is one whose diameter is the length of a side of the square. If the circle has radius r, then it has area (pi)r² and the square has area 4r², so the proportion of the square’s area that is wasted is (4-pi)/4 ~~ 21.46%.
Cutting a square from a circle.
The least wasteful (i.e. largest) square is one whose diagonal is a diameter of the circle. If the circle has radius r, then it has area (pi)r² and the square has area 2r², so the proportion of the circle’s area that is wasted is (pi-2)/pi ~~ 36.34%.
Cutting a circle from a square is thus less wasteful.