According to Plutarch, the Greeks found all the rectangles with
integer sides, whose areas are equal to their perimeters. Can you
find them? What rectangular boxes, with integer sides, have their
surface areas equal to their volumes?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
Catherine of Mount School, York and Joel of
ACS Barker, Singapore realised that it is not necessary to
calculate the lengths of the edges of the cuboid and they sent very
similar solutions. This is Catherine's solution:
Students from West Flegg Middle School,
Norfolk and Madras College, St Andrew's and Russell Lower School,
Ampthill also found the correct answer.