Question:

A hollow circular cylinder, open at one end, is constructed of thin sheet metal. The total external surface area of the cylinder is . The cylinder has a radius of and a height of .

(i) Express h in terms of r and show that the volume, , of the cylinder is given by:

Given that can vary,

(ii) Find the value of for which has a stationary value,

(iii) find this stationary value and determine whether it is a maximum or a minimum.

(i) Can someone please show me how to get ?