Solve the problem below. For your initial post in Brightspace, copy the description of your cylinder in the box below and then enter your solution to all three parts (parts a, b, and c) of the problem. To copy the description of your cylinder, highlighting and using "copy" from here in Mobius and then using "paste" into Brightspace should work.

Hint: This is similar to Question 63 in Section 5.7 of our textbook. We covered this section in "1-4Reading and Participation Activities: Inverses and Radical Functions" in Module One. You can check some of your answers to parts b and c to make sure that you are on the right track.

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)=

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.