Construct a cuboid with 24 small cubes, as shown opposite.

The surface area of the cuboid is

2 x (2 x 3 + 4 x 2 + 4 x 3) = 52 square units where the colours are top and sides

Does the surface area change if the arrangement (configuration) of cubes changes?

Problem 1   How many cubes are needed for the cuboid opposite?

Problem 2   Find the surface area of this cuboid.

Problem 3   Using 24 cubes to make a cuboid, what is the configuration that gives

                    a) minimum surface area

                                                                         b) maximum surface area?

Problem 4   Find the minimum wrapping for

                    a) 48 cubes                 b) 64 cubes.

Problem 5   For the cuboids you made earlier from 24 cubes, find the total length of string needed for each configuration.

Problem 6   What configuration minimises the amount of string needed to tie up a parcel of volume 24 cubic units?

1.   Find the cuboid shape that minimises the surface area when it encloses a fixed volume, V.

2.   Does this also minimse the string needed?