hidden faces

an exploration that considers surface area

a ppt is here

surface area and factorisable quadratrics

set up a quadratic equation
and solve it

a ppt is here

trial and improvement may well be speedier...
(but students shouldn't do that
because then they might neglect to find further solutions,
- even though there aren't any)

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

rubik cuboids and cubes

a ppt is here

(more shapes on the ppt)

cuboid surface area

a powerpoint (with more detail later on) is here

surface area for a given volume

a powerpoint is here

harder cuboid surface area questions

a ppt is here

this work can involve linear equations,
and quadratic equations for the last two














question 10 on the first sheet is demanding....

an intention is for students to try out the various multiples of 10
form an equation and solve it

however, there is a more complex and direct approach: