posted by Sarah on .
A florist uses wire frames to support flower arrangements displayed at weddings. Each frame is constructed from a wire length 9ft long that is cut into six pieces. the vertical edges of the frame consist of four of the pieces of wire that are each 12 inches long. one of the remaining pieces is bent into a square to form the base of the frame; the final piece is bent into a circle to form the top of the frame. how should the florist cut the wire of the length 9ft in order to minimize the combined area of the circular top and square base of the frame?
I'm not really sure what this is even asking.
I made a diagram according to you description and concluded the following
Since each of the 4 "verticals" is 12 inches, that would leave 5 feet or 60 inches for the circle and the square base
Let the radius of the circle be x feet
then the length for the base would be 5 - 2πx feet
and each side is 5/4 - (1/2)πx
let the total area of top and bottom be A
A = πx^2 + (5/4 - (1/2)πx)^2
differentiate, set that equal to zero and solve for x
I will let you finish the messy part.