Cuboid volume challenge
If you have a 20cm by 20cm piece of paper and you have to use it to make a box, what would be the dimensions of the box with the maximum volume?
This worksheet is a take on this traditional old classic lesson idea that combines some good mensuration, nets and calculation work with the spirit of investigation.
To extend or differentiate for higher attaining pupils you might like to use a cylinder shaped box rather than a cuboid. That way you could get in some work on circles too. If you wanted to focus on surface area, how about saying ‘what would be the dimensions of a box with the smallest surface area if the box had to have a volume of above X cm^2’?
The possibilities are endless with this one!