SOLUTION: A regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches. Approximately how many square centimeters of sheet metal will be left over as scraps?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches. Approximately how many square centimeters of sheet metal will be left over as scraps?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1028050: A regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches. Approximately how many square centimeters of sheet metal will be left over as scraps?
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
What is left over is the area of the circle minus the area of the hexagon...
A(circle) = %28pi%29r%5E2+=+36%28pi%29
A(hexagon) = 6%28s%5E2%2Asqrt%283%29+%2F+4%29+=+6%286%5E2%2Asqrt%283%29+%2F+4%29+=+54%2Asqrt%283%29
and
A(leftovers) = 36%28pi%29+-+54%2Asqrt%283%29=
19.57 sq cm