The height of the cylinder is 6 inches. We'll be analyzing the surface area of a round cylinder 7 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 Letgrbe the radius of the top of the can and lethhbe the height. The surface area of the cylinder, AA. is A=2nr2+2m=2nr2+2nrh [two circles, one for the top and one for the bottom plus a m rectangle for the sides}. r_= radius Areas = 1: r2. '1 = height >_ _" Q "- Are -_h(2rrr) Circumference 231' Part 3: Assume that the height of your cylinder is 66inches.C0nsiderAAas a function oft; so we can write that asA{r]=2nr2+12nrg=ZTrr2+121tr. What is the domain chang? In other words, for which values of g; is AMA; dened? Part b: Continue to assume that the height of your cylinder is 66 inches. Write the radius gas a function of AA. This is the inverse function to A[r]{1,r, i.e., to turn AA as a function of grinto gas a function of AA. IBEI Hints: - To calculate an inverse function. you need to solve for gr. Here. you would start with A=2nr2+12nr=2m2+121tr This equation is the same as err2+12nrA=021tr2+12nrA=Q which is a quadrch equation in the variable a; and you can solve that using the quadratic formula. You will want to keep AA as a variable when you plug the values into the quadratic formula. - Ifyou want to type in 3T[+1X+13'JI+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 300300 square inches. then what is the radius gr? In other words, evaluate gsooysoo. Round your answer to 2 decimal places. Hint: To compute a numeric square root such as 17.3\\f 17.3, you could - Use a spreadsheet such as Microsoft Excel or OpenOfce Calc and type in @113] - Use a browser to connect to the Internet and type in MI 7.3] into a search eld - Use a calculator The radius is inches if the surface area is 300300 square inches