The height of the cylinder is 4 inches.

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. Letrbe 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 is4inches.ConsiderAas a function ofr, so we can write that asA(r)=2r2+8r. 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 is4inches. Write the radiusras a function ofA. This isthe inverse function toA(r), i.e to turnAas a function ofrinto.ras a function ofA.

r(A)=

ab

sin(a)

Hints:

• To calculate an inverse function, you need to solve forr. Here you would start withA=2r2+8r. This equationis the same as2r2+8rA=0which is a quadratic equation in the variabler, and you can solve that using the quadratic formula.
• If you want to type in3+1x+1in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.

Part c: If the surface area is200square inches, then what is the rardiusr? In other words, evaluater(200).Round your answer to 2 decimal places.

Hint: To compute a numeric square root such as17.3, you could

• Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3)
• Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
• Use a calculator

The radius is inches if the surface area is200square inches.