The height of the cylinder is 4 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 r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A = 27W\"2 + 27rrh (it's two circles for the top and bottom plus a rolled up rectangle for the side). r = radius Areas = rt r3. h = height a, . Area = h(21tr) Circumference 2m Part a: Assume that the height of your cylinder is 4 inches. Consider A as a function of 'r, so we can write that as A (1') = 2 1'2 + 8 1W. What is the domain of A (r)? In other words, for which values of 1' is A (1\") dened? Part b: Continue to assume that the height of your cylinder is 4 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. 1' as a function of A. r(A)= 55D Hints: . To calculate an inverse function, you need to solve for 7'. Here you would start with 2 + 8 11'1\" A = 0 which is a quadratic equation in the variable 7', and you can solve that using the quadratic formula. 3;:11 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit. A = 2 7T'I'2 + 8 1w. This equation is the same as 2 1W- . If you want to type in Part c: If the surface area is 275 square inches, then what is the rardius r? In other words, evaluate 'r (275). 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 OpenOfce Calc and type in =sqrt(l7.3) - Use a browser to connect to the Internet and type in sqrt(l7.3) into a search eld 0 Use a calculator The radius is Number inches if the surface area is 275 square inches