



 
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 r^{2} + h × 2 π r cm^{2}. You know the surface area is to be 3000 cm^{2} and hence
The volume of a cylinder of radius r cm and height h cm is
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,  


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