The United States Navy wants to deploy a system of free floating sonar buoys. The electronics are contained in a spherical shell 2 feet in diameter that weights 300 pounds (shell plus equipment). A 4 foot long 4 inch diamter cylinder with radio transmitter and global positioning instrumnetation that weighs another 30 pounds is attached between the sphere with the electronics and the float. The Navy would like the center of the sphere to be suspended 6 feet below the surface of the water and the top of the float to be 6 inches above the water surface to minimize its radar image. The density of the float materail is 25 pounds percubic foot. The specific weight of sea water is 64 pounds per cubic foot.

The components are to be linked to one another with a uniqu linakge system that adds nothing to overall sphere-cylinder-float vertical dimension. What size float (length and diameter) is needed if the float is a cylinder with its longitudinal axis arranged veritically?