search for unusual cuboids

this involves work on the surface area and volume of a cuboid
the powerpoint is here

there are three tasks

• adding 1 to each of the (integer) dimensions, doubles the volume
• different cuboids with the same surface area and volume
• cuboids with the same value for the surface area and the volume (see lovely cuboids for a slightly different approach)

task 1

this task was offered by James Tanton

cuboids that double in volume when 1 is added to each of the (three) integer dimensions

task 2

different cuboids with the same surface area and volume

factors of the volume can be used to narrow the search

task 3

same value for surface area as volume

there are 10 altogether

see also lovely cuboids for a different approach to task 3