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 7' be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A = 2737-2 + 21r'r'h (it's two circles for the top and bottom plus a rolled up rectangle for the side). r = radius Areas = 1! r2. h = height 5 . Area = h(27rr) Circumference 2m 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 7W2 + 16 737'. What is the domain of A (7')? In other words, for which values of r is A (7") dened? 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 1' into. r as a function of A. 'r(A)= 'BB Hints: 0 To calculate an inverse function, you need to solve for 7'. Here you would start with 2 + 16 7' A = 0 which is a quadratic equation in the variable 7', and you can solve that using the quadratic formula. 3 1r+1 a3+1 more information in the Introduction to Mobius unit. A = 2 'mr'2 + 16 m". This equation is the same as 2 1r'r 0 If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is Part c: If the surface area is 200 square inches, then what is the rardius r? In other words, evaluate 7' (200) . Round your answer to 2 decimal places. Hint: To compute a numeric square root such as \\/ 17.3 , you could 0 Use a spreadsheet such as Microsoft Excel or OpenOfce Calc and type in =sqrt(l7.3) 0 Use a browser to connect to the Internet and type in sqrt(17.3) into a search eld 0 Use a calculator The radius is Number inches if the surface area is 200 square inches