A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.
I don't even know where to begin to find the relationship of height to radius of the sphere....
A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.
I don't even know where to begin to find the relationship of height to radius of the sphere....
Think of the problem in 2D. Center a circle on the Cartesian axes. draw a rectangle in it, also centered. with the edges touching the circle. think of this as viewing the cylinder in the sphere from sideways. now, do you knwo what you want to maximize?