Question

Find the dimensions of the rectangular box with largest volume if the total surface area is given as 16 cm2. (let x, y, and z be the dimensions of the rectangular box.) (x, y, z) =

Answer 1

The largest volume cuboid for a given surface area is a cube. The total surface area of a cube is 6 times the square of the length of one edge, so your dimensions are

  x = y = z = √(16/6) cm = (2/3)√6 cm, about 1.633 cm