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'Funnel' printed from http://nrich.maths.org/
section for detailed support for students, but
one of the main aims of this problem is to
use a spreadsheet to open up a problem that is otherwise rather
tedious to pursue by calculation. Students may need help thinking
through the calculation required and the spreadsheet commands
(formulae) necessary to achieve that. This is a challenging
The relationship between surface area and volume enclosed is an
important theme for able students at Stage 4 and using IT
effectively should be part of a good student's repertoire of
problem solving approaches.
With able students it is good to draw out that the ratio between
the volume and the surface area will change with scale, but the
optimum shape for the cone will not.
Perhaps reasoning in terms of units : measurements in a different
unit of length would change all the numbers (how ?) but not the
height-radius ratio (or cone angle) where the surface area takes
its minimum value.