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:

If the sides of the cuboid are x, y, and z and the areas of the rectangular faces are p, q and r then:

p = xy, q = yz and r = zx

It follows that pqr = (xy)(yz)(zx) = x

So the volume = xyz = sqrt (pqr) = sqrt (3 x 12 x 25) = sqrt 900 = 30

Students from West Flegg Middle School, Norfolk and Madras College, St Andrew's and Russell Lower School, Ampthill also found the correct answer.