A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let rbe the radius of the top of the can and lethbe the height.The surface area of the cylinder, A, isA=2?r2+2?rh(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 6 inches. Consider A as a function of r, so we can write that as A (r) = 2 ar- + 12 ar. 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 6 inches. Write the radius ~ as a function of A. This is the inverse function to A (r), i.e to turn A as a function of + into. ~ as a function of A. sin [2) ? (A) = Sip Hints: . To calculate an inverse function, you need to solve for r. Here you would start with A = 2 ar + 12 xr. This equation is the same as 2 ar- + 12 ar - A = 0 which is a quadratic equation in the variable y, and you can solve that using the quadratic formula. . If you want to type in 3 #$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 rardius r? In other words, evaluate - (150) . Round your answer to 2 decimal places. Hint: To compute a numeric square root such as v 17.3, you could Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sart(17.3)