A cube of edge length s is inscribed in a sphere of radius r.
(a) Write the surface area of a cube as a function of the radius r.
(b) Find the instantaneous rate of change of the surface area with respect to the radius r of the sphere.
(c) Evaluate the rate of change of the surface area at r = 2 and r = 8.
(d) If r is measured in millimeters and the surface area is measured in square millimeters, what units?