We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can".

A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let rbe the radius of the top of the can and lethbe the height.The surface area of the cylinder, A, isA=2r2+2rh(it's two circles for the top and bottom plus a rolled up rectangle for the side).

Part a: Assume that the height of your cylinder is 8inches.ConsiderAas a function ofr, so we can write that asA(r)=2r2+16r. What is the domain ofA(r)? In other words, for which values ofrisA(r)defined?

Part b: Continue to assume thatthe height of your cylinder is 8 inches. Write the radius ras a function of A. This isthe inverse function to A(r), i.e to turn Aas a function of rinto.ras a function ofA.

Part c: If the surface area is 150 square inches, then what is the rardiusr? In other words, evaluate r(150).Round your answer to 2 decimal places.