Nautical deck prism is a cylinder topped with a smaller cylinder which is topped by a hexagonal pyramid that was used to light the areas below deck during the day, before electricity. For one such "prism" the three pieces have the same volume. The bottom cylinder has a diameter of 3.5 in, the top cylinder has a diameter of 3.25 in, and the base of the pyramid is circumscribed by the top cylinder. a. (easier) If the bottom cylinder has a height of 0.5 in find the total height of the prism.
b. (more challenging) If the total height of the "prism" is 12 inches find the volume.