A cylinder (round can) has a circular base and a circular top with vertical sides in between. Letr be the radius of the top of the can and leth be the height.The surface area of the cylinder,A, isA=2r^2+2rh(it's two circles for the top and bottom plus a rolled up rectangle for the side).

Part a: Assume that the height of your cylinder is4inches.ConsiderA as a function ofr, so we can write that asA(r)=2r2+8r. What is the domain ofA(r)? In other words, for which values ofr isA(r) defined?

Part b: Find the inverse function toA(r). Your answer should look liker="some expression involvingA". Hints:

• To calculate an inverse function, you need to solve forr
• Here you could start withA=2r2+8r. This equationis the same as2r2+8rA=0. Do you recognize this as a quadratic equationax2+bx+c=0 where the variablex isr? The coefficients would be2 fora,8 forb,andAforc You can solve forrusing the quadratic formula even though the constant termcis a symbol here.

Part c: If the surface area is325square inches, then what is the radiusr? In other words, evaluater(325).Round your answer to 2 decimal places.