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 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. Let rr be the radius of the top of the can and let hh be the height. The surface area of the cylinder, AA, is A=2πr2+2πrhA=2πr2+2πrh (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 is 66 inches. Consider AA as a function of rr, so we can write that as A(r)=2πr2+12πrAr=2πr2+12πr. What is the domain of A(r)Ar? In other words, for which values of rr is A(r)Ar defined?   Part b: Continue to assume that the height of your cylinder is 66 inches. Write the radius rr as a function of AA. This is the inverse function to A(r)Ar, i.e to turn AA as a function of rr into. rr as a function of AA.   r(A)=rA=   ab sin(a) ∞ α                Hints: To calculate an inverse function, you need to solve for rr. Here you would start with A=2πr2+12πrA=2πr2+12πr. This equation is the same as 2πr2+12πr−A=02πr2+12πr−A=0 which is a quadratic equation in the variable rr, and you can solve that using the quadratic formula. If you want to type in 3π+1x+13π+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 125125 square inches, then what is the rardius rr? In other words, evaluate r(125)r125. Round your answer to 2 decimal places. Hint: To compute a numeric square root such as 17.3−−−−√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  inches if the surface area is 125125 square inches.