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 (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).

A round cylinder with a circle top and base with radius r and a height of h



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)=2πr2+16πr . What is the domain of A(r) ? In other words, for which values of r is A(r) defined?



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 .



r(A)=
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Hints:

To calculate an inverse function, you need to solve for r . Here, you would start with A=2πr2+16πr . This equation is the same as 2πr2+16πr−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 3π+1x+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.


Part c: If the surface area is 100 square inches, then what is the radius r ? In other words, evaluate r(100) . 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 100 square inch