Name_____________________________

Lab Section: _____________

Worksheet for Size and Shape in Biology Tutorial

1. Scaling of cubes: fill in the table
   
   

   	small cube	medium cube	large cube
   length (cm)
   surface area (cm2)
   volume (cm3)
   surface area/volume
   surface area/length
   volume/length

   
   
   
2. How big could a sugar cube get before the bottom crushed under its own weight?
   

   	useful info:	density = 1040 kg/m3
   		crushing strength = 5.17x106 N/m2
   		acceleration due to gravity = 9.81 m/s2

   
   
   
   
   
   
   
   
   
   
3. For each of the four examples below, the slope of a power function is given comparing two measurements of a group of organisms. For each, give the slope you would expect if the relationship is isometric, and state whether the observed relationship is isometric or allometric. The log of the first variable would be plotted on the y-axis and the log of the second on the x-axis.
   1. arm length vs. body height for infant humans: b=1.2
      
      
      
      
   2. brain mass vs. body mass in humans: b=0.66
      
      
      
      
   3. mass of skeleton vs. body length in whales: b=3.07
      
      
      
      
   4. mass of skeleton vs. body length in terrestrial mammals: b=3.25
      
      
      
      
      
      
4. Professor LaBarbera's house (10m wide, 20m long, 4m high - just a hovel, really) has a 30,000 watt furnace that just barely keeps him warm on cold Chicago nights. He's thinking of building a larger house to accommodate his growing collection of abalone shells, and needs advice on the output of the new furnace. The new house will be 3 times as high, 3 times as wide, and 3 times as long.
   1. If he assumes that the furnace size should be proportional to the volume of the house, then what size furnace should he install?
      
      
      
      
      
      
   2. If heat loss depends on the surface area of exterior walls, roof, and floor exposed to the winter cold rather than on the volume of the house, then what size furnace would you recommend?
      
      
      
      
      
      
5. Mammals are endothermic, maintaining fairly constant high body temperature by their metabolism. Metabolic rate is a measure of the heat production (and thus heat loss) of an organism.
   1. If resting metabolic rate is proportional to the mass of tissue in an animal, then what would be the slope of a graph of log(resting metabolic rate) vs. log(mass)?
      
      
      
      
      
   2. Some studies have found this slope (within one species) to be 2/3. Propose a hypothesis to account for this based on the principles explored in the home furnace question.
      
      
      
      
      
   3. Given the observed relationship between metabolic rate and size, what differences might you find in equivalent-sized cells from a mouse and an elephant?