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)=






Change entry mode
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.
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 125
square inches, then what is the rardius r
? In other words, evaluate r(125)
. 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 125
square inches.