A cylinder (round can) has a circular base and a circular top with vertical sides in between. Letrbe the radius of the top of the can and lethbe 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 is6inches.ConsiderA as a function ofr, so we can write that asA(r)=2r^2+12r. What is the domain ofA(r)? In other words, for which values ofrisA(r) defined?

Part b: Continue to assume thatthe height of your cylinder is6inches. Write the radiusr as a function ofA. This isthe inverse function toA(r), i.e to turnAas a function ofrinto.ras a function ofA.

Hints:

To calculate an inverse function, you need to solve forr. Here you would start withA=2r^2+12r. This equationis the same as2r^2+12rA=0 which is a quadratic equation in the variabler, and you can solve that using the quadratic formula.

Part c: If the surface area is100square inches, then what is the rardiusr? In other words, evaluater(100).Round your answer to 2 decimal places.