A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 40 cm3. If nickel plating costs $1 per cm2 and silver plating costs $12 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length _______ cm and a height of________ cm.