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 material in the Module One section "Inverses and Radical Functions" within the Reading and Participation Activities. 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 8 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. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (it's two circles for the top and bottom plus a rolled up rectangle for the side).

A round cylinder with a circle top and base with radius r and a height of h

Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+16πr . What is the domain of A(r) ? In other words, for which values of r is A(r) defined?

Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A . This is the inverse function to A(r) , i.e to turn A as a function of r into. r as a function of A .

r(A)=

Change entry mode
Hints:

To calculate an inverse function, you need to solve for r . Here you would start with A=2πr2+16πr . This equation is the same as 2πr2+16πr−A=0 which is a quadratic equation in the variable r , and you can solve that using the quadratic formula. If you want to type in 3π+1x+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 is 250 square inches, then what is the rardius r ? In other words, evaluate r(250) . Round your answer to 2 decimal places.

Hint: To compute a numeric square root such as 17.3−−−−√ , 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 3.47 inches if the surface area is 250 square inches.