Ms Rowe needs to make a box to hold 729 cm^3. She needs the box to have a lid. What are the dimensions of the box that would minimise the surface area?

If the dimensions are x,y,z, you need to find the minimum of

2xy+2xz+2yz
using xyz=729

I think you will find that a cube does the job, just as a square minimizes the perimeter for a given area.