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?