The height of the cylinder is 4 feet.

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. Since the top and bottom both are circles with radius r, the areas of the top and bottom both are πr2. You can think of the side as a rolled up rectangular piece that is h long by (the circumference of the circle) 2πr wide, so the side has a total area of h(2πr)

Thus the surface area of the cylinder, A, is A=2πr2+2πrh.

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). What is the domain and range of A(r)?

Part b: Continue to assume that the height of your cylinder is 4 inches. Write the radius r as a function of A. This is the inverse function to A(r), i.e. r as a function of A or r(A). What is r(A) and what is the domain and range of r(A)? What is r(A)? (Do not include the units "inches" in your answer.)

Hints: Mobius accepts the following ways to type in mathematics:

To enter a square root such as x+3−−−−−√, you can type in sqrt(x+3)
To enter the number π, you can type in pi
To enter a division such as x+3y+1, you can type in (x+3)/(y+1)
Remember to use parentheses for order of operations!
Part c: If the surface area is 175 square inches, then what is the rardius r? 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 *number* inches if the surface area is 175 square inches