The height of the cylinder is 6 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. Letr

be the radius of the top of the can and leth

be the height.The surface area of the cylinder,A

, isA=2r

2

+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 is6

inches.ConsiderA

as a function ofr

, so we can write that asA(r)=2r

2

+12r

. What is the domain ofA(r)

? In other words, for which values ofr

isA(r)

defined?

Part b: Continue to assume thatthe height of your cylinder is6

inches. Write the radiusr

as a function ofA

. This isthe inverse function toA(r)

, i.e to turnA

as a function ofr

into.r

as a function ofA

.

r(A)=

Hints:

• To calculate an inverse function, you need to solve forr
• . Here you would start withA=2r
• 2
• +12r
• . This equationis the same as2r
• 2
• +12rA=0
• which is a quadratic equation in the variabler
• , and you can solve that using the quadratic formula.
• If you want to type in3+1
• x+1
• in 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 is200

square 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 isinches if the surface area is200

square inches.