Once the lower level thinking covered in the Hint has been assimilated students might be guided if necessary to see the value of a spreadsheet when solving a problem of this sort.

Additionally the use of a graph representing the spreadsheet values is particularly helpful for 'picturing' the behaviour of the surface area function as either base radius or can height varies.

There is a valuable opportunity to work with each of the two obvious independent variables : base radius and height. Starting with either of these the other is calculable from the specified volume of 330 ml, and once both r and h are known the surface area is calculable.