Hi Haris,

The surface of the cylinder is composed of two circular disks of radius r cm each and the side of the cylinder which can be cut from bottom to top and rolled out to form a rectangle. (Think of the label on a soup can.) The rectangle has height h cm and its length is the circumference of the circular top which is 2 π r cm. The surface area of the cylinder is then 2 × π r² + h × 2 π r cm². You know the surface area is to be 3000 cm² and hence

2 π r² + 2 π r h = 3000 cm²                    (1)

The volume of a cylinder of radius r cm and height h cm is

V = π r² h cm³                                       (2)

Solve equation (1) for h and substitute into equation (2). This will give an expression for the volume in terms of r alone. Use the calculus you know to maximize V.

I hope this helps,
Penny