Here is the problem that I was given:
The height of the cylinder is 4 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=2πr2+2πrh (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 is 4 inches. Consider A as a function of r, so we can write that as A(r)=2πr2+8πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined? (-infinity, infinity) I came up with this answer by knowing that the domain for r is any value that whether its positive, negative or zero.
Part b: Continue to assume that the height of your cylinder is 4 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. The answer I came up with for this portion of the question is: --2+/-sqrt(16*Pi^2+2*Pi*A)/2*Pi. I used the quadratic formula to answer this portion of the question. This portion of the question gave me some issues. I’m pretty confident that I got it right but on Mobius no matter how I tried to enter it, it kept saying it was incorrect. I’ve issues in the past with Mobius being very picky with how things get entered(especially +/-, which I have in my answer). So, I don’t know whether I’m wrong or Mobius is being picky.
Part c: If the surface area is 175 square inches, then what is the radius r? In other words, evaluate r(175). Round your answer to 2 decimal places.
I got my answer by plugging in 175 into this equation:
--2+/-sqrt(16*Pi^2+2*Pi*A)/2*Pi
--2+/-sqrt(16*Pi^2+2*Pi*175)/2*Pi
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2+/- 35.4608389494664945/2*Pi = -2 +/- 5.6437678
So, the answer for the radius is 5.64 +/- 2.
