Please help! I had the radius as 5.19 and part b as [0,+infinity), but I apparently I am wrong! Thank you in advance!

The height of the cylinder is 6 inches.

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. The surface area of the cylinder, A, is A=2r2+2rh (it's two circles for the top and bottom plus a rolled up rectangle for the side).

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 4 inches. Consider A as a function of r, so we can write that as A(r)=2r2+8r. What is the domain of A(r)? In other words, for which values of r is A(r) defined?

Part b: Find the inverse function to A(r). Your answer should look like r="some expression involving A".

r(A)=

Part c: If the surface area is 300 square inches, then what is the radius r? In other words, evaluate r(300). Round your answer to 2 decimal places.

The radius is______ inches if the surface area is 300 square inches.