2. invasion of the Giant Worms from Outer Spoce! You have likely encountered a common earthworm (Lumbricus terrestrial some point in your life. The earthworm absorbs oxygen directly through its skin, and it has a good circulatory system (with multiple small hearts) that brings the oxygen to all the cells. However, the worm's cells are distributed throughout its volume, while the oxygen only comes into the worm through the skin. Therefore, the ratio of the worm's surface area to its volume plays an important role in determining a worm's size. We will see how this works by applying modeling and scaling to the biological system of the earthworm. 3. We are interested only in the physical size of a worm, so we will model the worm using a simple geometric shape. What shape (e.g., sphere, cube, etc.) would be most appropriate? Cylinder b. Write equations for the surface area and the volume of the worm using _ to represent the worm's length and R to represent its radius. (For the surface area, you can neglect the circles at the ends of the worm.) Surface area : ZaRL VOLUME : TRIL LE worms langit c. What would be a reasonable order of magnitude estimate for the length of a worm in meters? Or did 10em - length 10 d. What would be a reasonable order of magnitude estimate for the diameter of a worm in meters? 0.50cm - diameter C. Using your equations in part b and your estimates in parts c and d, calculate the surface area and volume of a worm. (Note that radius is half the diameter. Do the calculations exactly, not as estimates, so include numbers like 2 and 7} Surface area . 2TRL volume . TIR ZL 2 63.14) (10em) (0.25 cm) (8-14)1 0.26 emil [IDem) 2 68-147 (0-1m) (0-0025m) - 1-46 cm 3 = 0. 00157m' 1 1.96 *10 -6 cma = 1540m f. Determine the area and volume of the warm as order of magnitude estimates by rounding your answers in parce to the nearest power of 10 Cell shape : sphere & find cell shape ? V = 4 - sphere? 4 (3.14 ) ( # * 10 - 5m) ' area = (3.14 ) (0.125 x 10-15) : 0. 523 x10 -15 m 3