Question

I need help on an optimization problem of a cylinder within in a sphere. I will post document with question and work done so far.

Answer 1

Question 5. A right circular cylinder is inscribed in a sphere of radius R. Find the largest
possible surface area of such cylinder.

Answer 2

go to google and search cylinder inside a sphere

Answer 3

\[S = 2\pi x^{2} + 2\pi x(2y)\]