Hello guys.....i am really struggling with the following problem!!!! I have got exam in 2 days and the following question is from the preliminary exam sheet. Please help.
Heres the question:
A piston moves freely in a cylinder of radius r and height h. It is desireable for the surface of the cylinder above the piston to be kept to a minimum.
If the volume of this space is to be 500 c.c., find the values for the radius and height that give us the minimum surface area.
-Using the known volume write down a formula for h in terms of r. Write down a formula for the surface area in terms of r only.
- Using calculus, find the radius where a turning point occurs. Determine whether this radius produces a maximum or minimum surface area.
I am attaching a picture of this question!!!!
I seriously havent got a clue on what to do.