The surface of a rotating cylinder of fluid takes on a parabolic shape. Engineers have used that fact to produce large telescope mirrors using mercury as the liquid. You propose to make a 3-meter telescope mirror from mercury using a similar approach.

a. If the focal length of the mirror is to be six times the mirror's diameter, how fast would one need to rotate the container of mercury?

b. What would be the minimum volume of mercury required to make the mirror? How much would it weigh?