Maximum surface area of a cylinder inscribed in a sphere of radius R

[rishiraj20006]

How would we find the maximum surface area of a cylinder inscribed in a sphere of radius R. This problem is given in my textbook . I know concept of maxima and minima will be apllicable here but i can,t start and make the expression of surface area in a suitable manner. Anybody having answers

 

[quasar987]

Start by determining what will be the relation (equation) between the radius of the cylinder and it's lenght, given that it is inscribed in the sphere. With that you can write the equation of the area of the cylinder as a function of 1 variable only (radius or lenght), and solve for the max.

 

[HallsofIvy]

First draw a picture! Your picture should be of a circle (the sphere seen from the side) with a rectangle (the cylinder) inside it. If you set up a coordinate system with (0,0) at the center of the circle, you should be able to find either of h and r of the cylinder as a function of the other. (The Pythagorean theorem is helpful here.)