Designing your perfect swimming pool

My extension students were asked this week to find the volume of an average swimming pool that is 3-6 metres wide, 6-12 metres long, and 1-3 metres deep.  Once they worked out the volume of 81 cubic metres, they were asked to work backwards and design their perfect swimming pool with exactly that volume.  What they came up with was nothing short of amazing.

One student chose to design a circular dive pool, so they worked with a fixed 3m depth and calculated the diameter (5.86m).  

Another designed an upside down square pyramid shape that was at most 2m deep.  They had to understand the relationship between the volume of a pyramid and the corresponding prism (1/3), and then calculate the length of the side (11.02m).  

The third student chose to design their pool in the shape of a capital E.  Rather than choosing their preferred depth, this student chose a length and width they liked, found the surface area of the block-letter E, then worked out how deep their pool would need to be to have the required volume.  All three did outstanding work that was tricky to draw, hence the lack of photos.

If you know anyone who is inspired by challenging themselves to do Maths like this, please let me know.  I'd love a few more bright sparks to join us.