Activity 3: Why insects can’t be big? 50 points Model 1: Surface area-­‐to-­‐volume ratios 1. The surface area of a cube is expressed by the equation: # of sides × length × width, or 6x2, where 6 = the number of sides and x = the length of any edge. What is the surface area of each of the three cubes shown above in Model 1? Show your work. (3 points) 1 mm cube surface area: 2 mm cube surface area: 4 mm cube surface area: 2. The volume of a cube is expressed by the equation: x3, where x = the length of any edge. What is the volume of each of the three cubes shown above? Show your work. (3 pts) 1 mm cube volume: 2 mm cube volume: 4 mm cube volume: 3. The surface area-­‐to-­‐volume ratio of a cube is expressed by the equation: surface area ÷ volume. What is the surface area-­‐to-­‐volume ratio of each of the three cubes shown above? Show your work. (3 points) 1 mm cube surface area-­‐to-­‐volume ratio: 2 mm cube surface area-­‐to-­‐volume ratio: 4 mm cube surface area-­‐to-­‐volume ratio: 4. Using the information you just derived in Question 3 about surface area-­‐to-­‐volume ratio, write a sentence that describes what happens to the surface area-­‐to-­‐volume ratio of a cube as it gets larger. Be VERY precise in how your word this sentence. (3 points) 5. Now consider an arthropod such as a terrestrial insect. A key feature of an arthropod is its exoskeleton. What happens to the exoskeleton (i.e. the surface area) to size (volume) ratio as the insect increases in size (i.e. volume)? (4 points) 6. What design problem is inherent in having an exoskeleton that increases at a slower rate than body mass? (Consider the functions of the exoskeleton for respiration and structural support, as well as your answer to Questions 4 to help you think about this answer.) (4 points) Model 2: Diffusion of molecules 7. Look at Model 2. Over time, what happens to the molecules of dye that are dropped into the left side of the beaker? (2 points) 8. Is external energy (e.g. stirring or pumping) needed to move the molecules of dye around? (2 points) 9. In your own words, write a complete sentence defining diffusion. (4 points) 10. In your own words, write a complete sentence defining equilibrium as seen in Model 2. (4 points) Model 3: An insect’s tracheal system 11. Now that you understand how molecules move from areas of high concentration to areas of low concentration, consider an insect’s tracheal system. On the diagram above, draw molecules of oxygen (designated as “O2”) to indicate its diffusion in this system. Indicate areas of high O2 concentration, low O2 concentration, and draw arrows to indicate the direction of O2 diffusion. (2 points) 12. On the diagram above, draw molecules of carbon dioxide (designated as “CO2”) to indicate its diffusion in this system. Indicate areas of high CO2 concentration, low CO2 concentration, and draw arrows to indicate the direction of CO2 diffusion. (2 points) 13. If an insect’s respiratory system relies entirely on the passive diffusion of oxygen from the external environment to individual cells, describe how this might become a problem as insects increase in size. (4 points) Exceptions to the rule 14. Why can some arthropods, such as king crabs, get so large in the ocean? (Hint: how might living in a cold water environment help to overcome both of the size restrictions that you worked through above?) (5 points) 15. Why were some extinct terrestrial arthropods able to get so much larger than any extant terrestrial arthropods? (Hint: how was the atmosphere different than it is now?) (5 points) 16. What questions do you still have about why insects are limited to being fairly small organisms?