Hello Maths Methods CAS,
I'm not doing methods, but I had a look at your 'cone of death' just before and it seem to me that there was a much more simple way to solve it than you guys did... you can do it graphicaly.
Because of the shape of the cone, the cylinder is held in such a way that when the height is 0, the radius is 2, and when the radius is 0 the height is 5. This gives you this:
Height: 0 Radius: 2
Height: 5 Radius: 0
You can then use those to plot a graph (the fist set of numbers being x1, y1 and the seccond set beign x2, y2)
The equation of that graph (using y=mx+c) is (with h on the y axis): h= -5/2 r +5
This is essentialy the same as the equation you find using your simmilar triangles method isn't it?
I may be completely wrong, so correct me if I am... but it seems to be a more simple way.