Make an open-top box from a rectangle of cardboard 9 by 15 inches by cutting a square from each corner and folding up the sides. The box needs to have the maximum possible volume.

If each square you cut out of the corner is x by x inches, write an expression or function for the volume of the box, V(x), in terms of x. Show all your work.

Plot the function to find the maximum. Clearly label or state the (x, y) coordinates of the value of x that optimizes the function and the maximum volume (y).

How many pennies would it take to fill the box?

For 10 points!