I've spent a few hours at this question but can't seem to get the right answer. I was hoping someone here can lead me in the right direction.
The question:
A storage tank is to be constructed in the shape of a cylinder such that the ratio of the radius, r, to the height of the tank is 1: 3. Write a polynomial function to represent the surface area of the tank in terms of r.
What I've Tried: https://i.stack.imgur.com/nMUwn.jpg
The correct answer is $$f(r)=(6\pi r^2)(r+1).$$
I've tried Googling it and asking friends but still haven't come to the right answer. Any help would be greatly appreciated.
Thank you very much!
The answer you state as "correct" is wrong. You check this through unit analysis: If radius and height are given in meters, the expression $r+1$ adds meters to a pure number, which is meaningless. Since you want area, the unit should become meters squared.
Your next-to-last line was correct: just finish the simplification for the really correct answer.
$$f(r)=2\pi r^2+6\pi r^2$$ $$=8\pi r^2$$
You can see that this has the right dimensions.