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=2πr2+2πrh (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 4 inches. Consider A as a function of r, so we can write that as A(r)=2πr2+8πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined?   Part b: Find the inverse function to A(r). Your answer should look like r="some expression involving A".   r(A)=       Hints: To calculate an inverse function, you need to solve for r. Here you could start with A=2πr2+8πr. This equation is the same as 2πr2+8πr−A=0. Do you recognize this as a quadratic equation ax2+bx+c=0 where the variable x is r? The coefficients would be 2π for a, 8π for b, and −A for c. You can solve for r using the quadratic formula even though the constant term c is a symbol here.   Part c: If the surface area is 275 square inches, then what is the radius r? In other words, evaluate r(275). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as 17.3−−−−√, you could Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3) Use a browser to connect to the Internet and type in sqrt(17.3) into a search field Use a calculator   The radius is  inches if the surface area is 275 square inches.