Maximise a complete globe on a closed cylindrical base

A decorative monument for the 2010 Youth Olympic Games consists of a complete globe on a closed cylindrical base of radius $r$ and height $h$. The globe radius is $1.25r$. To minimise cost, the total surface area is fixed at $36.5\text{ m}^2$.

(i) Show that $h=(146-33\pi r^2)/(8\pi r)$.2 marks

Hence find exactly:

(ii) the cylinder radius giving greatest total volume.7 marks

(iii) that maximum volume.2 marks

A sphere of radius $R$ has area $4\pi R^2$ and volume $4\pi R^3/3$.