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.

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.