Suppose that we want a cylindrical barrel to hold 88 cubic feet of volume. Let the barrel have radius rr and height h,h, each measured in feet. How can we write the surface area, A,A, of the barrel solely as a function of r?

• Draw several possible pictures of how the barrel might look. For instance, what if the radius is very small? How will the height appear in comparison? Likewise, what happens if the height is very small?
• Use the fact that volume is fixed at 88 cubic feet to state a constraint equation and solve that equation for hh in terms of r.r.
• Recall that the surface area of a cylinder is A=2πr2+2πrh.A=2πr2+2πrh. Use your work in (c) to write AA as a function of only r.r.
• What is the domain of A?A? Why?
• Explain why AA is not a polynomial function of r.

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