3. We can model a bacillus (rod-shaped bacterium) as a cylinder for simplicity. Measure the length ("height") and radius in micrometers. (a) Determine the greatest volume that a cylinder with surface area 6007 um could have. (b) Determine the minimal surface area needed for a cylinder with volume 10247 um3. (c) For each of parts (a) and (b), describe the ratio of diameter to height that produces the optimal cylinder