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 = 271'7'2 + 27r7'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. h = height Area = h(2nr) Circumference 2m Part 3: 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 7T1'2 + 16 arr. What is the domain of A (r)? In other words, for which values of 1' is A (7') dened? Part D: 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 7' as a function of A. r(A)= QED Hints : 0 To calculate an inverse function, you need to solve for 'r. Here, you would start with A = 2 W2 + 16 71'7". This equation is the same as 2 1TT2 + 16 W A = 0 which is a quadratic equation in the variable 7', 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. 3 1r+1 93+ 1 is more information in the Introduction to Mobius unit. 0 If you want to type in in Mobius, in text mode you can type in (3*pi+l)/(x+l). There Part c: 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 \\/ 17.3, you could 0 Use a spreadsheet such as Microsoft Excel or OpenOfce Cale and type in =sqrt(l7.3) 0 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 250 square inches