We'll be analyzing the surface area of a round cylinder - in other words, the amount of material needed to "make a can".

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We Ll Be Analyzing The Surface Area Of A Round Cylinder In Other Words The Amount Of Material Needed To Make A Can 1 (214.85 KiB) Viewed 51 times

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 + 2ærh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides). r = radius Areas = r² r Circumference 2πr Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can write that as A (r) = 2 ær² + 12 r. What is the domain of A (r)? In other words, for which values of r is A (r) defined? (A) h = height Part b: Continue to assume that the height of your cylinder is 6 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 intor as a function of A. Area = h(2πr) Hints: • To calculate an inverse function, you need to solve for r. Here, you would start with A 2 πη2 + 12 π. = This equation is the same as 2 πη2 + 12 mr . 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 π+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). x+1 There is more information in the Introduction to Mobius unit. Part c: If the surface area is 325 square inches, then what is the radius r? In other words, evaluate r (325). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as √17.3, you could The radius is Number • 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 325 square inches.