21. AJ wants to be an engineer when he grows up. He started tinkering with electronics last year and has a design for a battery in mind. Part of his design includes a cyclindrical coil of copper wire inside a spherical shell. Given a spherical shell of radius r, AJ wants to maximize the volume enclosed by the copper coil. i. (2 points) How might the radius r of the sphere be expressed in terms of R and h? ii. (2 points) Let R be the radius of the circular base of the cylindrical coil and h the height. The volume V enclosed by the cylindrical coil expressed in terms of R and h is V = TRh. How might V be rewritten as a function of h? iii. (6 points) Show that the dimensions of the cylindrical coil which encloses the largest possible volume is h = and R = 1413