Mastering Mathematics Smartly
by Wee Wen Shih

Many students may have forgotten the good old concept of similar triangles that they learnt at O-level. Interestingly, schools like to ask questions that require the use of this idea, say in questions related to maxima/minima and rates of change.

We discuss a worked example here in order to refresh your memory.

Give this question a try:
A cone with height h is inscribed in a larger cone with a height H so that its vertex is at the center of the base of the larger cone. Show that the inner cone has a maximum volume when h = (1/3)H.