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 I: be the height. The surface area of the cylinder, A, is A = Zara-2 + 21r'r'h (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides). r_- radius Areas = rt r2: __3' h = height Area = h(2n:r) Circumference 2m" Part 3: Assume that the height of your cylinder is 4 inches. Consider A as a function of r, so we can write that as A (r) = 2 m2 + 8 arr. What is the domain of A (r)? In other words, for which values of r 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 (5"), i.e., to turn A as a function of'r into 1' as a function of A. Hints: - To calculate an inverse function, you need to solve for 1'. Here, you would start with 2 A = 2 71-1-2 + 8 171'. This equation is the same as 2 m- + 871'? A = l] which is a quadratic equation in the variable 1', 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. 1r+l 3+1 more information in the Introduction to Mobius unit. - If you want to type in in Mobius, in text mode you can type in (3*pi+1)f{x+l). There is Part I: If the surface area is 250 square inches, then what is the radius r? In other words, evaluate r{250). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as V173, you could - Use a spreadsheet such as Microsoft Excel or OpenOfce Cale and type in =sqrt{1':'.3) - Use a browser to connect to the Internet and type in sqrt(1?.3) into a search field 0 Use a calculator The radius is Number inches if the surface area is 250 square inches