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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 = 2xr² + 2arh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides). Areas = ¹² T (A) = r-radius Circumference 2x 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) = 2 72 +8 r. What is the domain of A (r)? In other words, for which values of is A (r) defined? . h-height Part b: Continue to assume that the height of your cylinder is 4 inches. Write the radius as a function of A. This is the inverse function to A (r), i.e., to turn A as a function of intor as a function of A. Area =h(2m) Hints: To calculate an inverse function, you need to solve for r. Here, you would start with A = 2² +8 r. This equation is the same as 22 +8r-A=0 which is a quadratic equation in the variable r, 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. • If you want to type in 3+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit. The radius is Number Part c: If the surface area is 150 square inches, then what is the radius? In other words, evaluate r(150). 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 inches if the surface area is 150 square inches.