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 "1-3 Reading and Participation Activities: Models and Applications" 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 feet.

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.Since the top and bottom both are circles with radiusr , the areas of the top and bottom both arer2. You can think of the side as a rolled up rectangular piece that ish long by (thecircumference of the circle)2r wide,so the sidehas a total area ofh(2r)

Thus the surface area of the cylinder,A , isA=2r2+2rh.

Part a: Assume that the height of your cylinder is4inches.ConsiderA as a function ofr, so we can write that asA(r) . What is the domain and range ofA(r)?

Part b: Continue to assume thatthe height of your cylinder is4

inches. Write the radiusr as a function ofA This isthe inverse function toA(r) , i.e.ras a function ofAorr(A). What isr(A) and what is the domain and range ofr(A)? What isr(A)? (Do not include the units "inches" in your answer.)

Hints: Mobius accepts the following ways to type in mathematics:

• To enter a square root such asx+3
• , you can type in sqrt(x+3)
• To enter the number
• , you can type in pi
• To enter a division such asx+3
• y+1
• , you can type in (x+3)/(y+1)
• Remember to use parentheses for order of operations!

r(A)=------------------------- answer

Part c: If the surface area is100 square inches, then what is the r as radiusr? 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 ------------ answer inches if the surface area is100square inches.