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 y be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A =2x2+ 2xrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides). r = radius Areas - T r- h = height Area = h(2mr) Circumference 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) = 2 ar2 + 16 wr. What is the domain of A (r)? In other words, for which values of T 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) = Hints: . To calculate an inverse function, you need to solve for r. Here, you would start with A = 2 x2+ 16 xr. This equation is the same as 2 my- + 16 ar - A =0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula. . If you want to type in 3 7+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 150 square inches, then what is the radius ? In other words, evaluate r (150). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as v17.3, 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 Number inches if the surface area is 150 square inches