A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the

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A Cylinder Round Can Has A Circular Base And A Circular Top With Vertical Sides In Between Let R Be The Radius Of The 1 (229.7 KiB) Viewed 47 times

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 + 2árh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides). r = radius Areas = π r² r(A) Circumference 2лr Part a: 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 T² + 16 r. What is the domain of A (r)? In other words, for which values of r is A (r) defined? = h = height Part b: 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 r as a function of A. 2 πρ Area = h(2) - Hints: • To calculate an inverse function, you need to solve for r. Here, you would start with A = 2 πr² πησ + 16 mr. This equation is the as 2 + 16 πr - 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 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit. 3 π+1 x+1 The radius is Number Part c: If the surface area is 300 square inches, then what is the radius r? In other words, evaluate r (300). 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) same • 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 300 square inches.