Surface to Volume Ratios
•Big animal
•Large surface area
•Big rug
•Small animal
•Small surface area
•Small rug
Surface Area = Length X Width X Number of Sides
Volume = Length X Width X Height
1 centimeter cube
Surface area = 1 cm X 1 cm X 6 = 6 cm2
Volume = 1 cm X 1 cm X 1 cm = 1 cm3
Surface to Volume Ratio: 6/1 or 6:1 (6 parts surface
area exposed per unit volume)
Surface Area = Length X Width X Number of Sides
Volume = Length X Width X Height
2 centimeter cube
Surface area = 2 cm X 2 cm X 6 = 24 cm2
Volume = 2 cm X 2 cm X 2 cm = 8 cm3
Surface to Volume Ratio: 24/8 or 3:1 (3 parts surface
area exposed per unit volume)
Surface Area = Length X Width X Number of Sides
Volume = Length X Width X Height
3 centimeter cube
Surface area = 3 cm X 3 cm X 6 = 54 cm2
Volume = 3 cm X 3 cm X 3 cm = 27 cm3
Surface to Volume Ratio: 54/27 or 2:1 (2 parts surface
area exposed per unit volume)
1 centimeter cube
Surface area = 1 cm X 1 cm X 6 = 6 cm2
Volume = 1 cm X 1 cm X 1 cm = 1 cm3
Surface to Volume Ratio: 6/1 or 6:1 (6 parts surface area exposed
per unit volume)
2 centimeter cube
Surface area = 2 cm X 2 cm X 6 = 24 cm2
Volume = 2 cm X 2 cm X 2 cm = 8 cm3
Surface to Volume Ratio: 24/8 or 3:1 (3 parts surface area exposed
per unit volume)
Surface to
Volume Ratio
Size of Cube
Surface Area
Volume
1 cm
6 cm2
1 cm3
6:1
2 cm
24 cm2
8 cm3
3:1
3 cm
54 cm2
27 cm3
2:1
Surface to Volume Relationship
• The larger the animal the lower the amount of
surface area exposed in proportion to volume.
– Thus there is less heat loss through the skin per
unit volume
• The smaller the animal the greater the
amount of surface area exposed in proportion
to volume.
– Thus small animals lose more heat per unit
volume than large animals.
Due to their small size hummingbirds have a huge
problem with heat loss if environmental
temperatures are cold.
Torpor
The rufous hummingbird weighs about 3 grams, roughly the same as a penny.
Heart rates: Resting = 250 beats per minute
Feeding = 1200 beats per minute
Body Temperature: 105 – 1080F
Bermann’s Rule
• As you go up in elevation or you move
towards the poles the temperature?________
• As you go up in elevation you move towards
the poles you would expect the body size (or
average weight) of an animal to?_________
Bergmann's rule (“B” = Body Size)
• Big animals → have larger body masses → more heat is being
produced.
• The more cells an animal has → more internal heat will be produced.
• Big animals → have a smaller surface area exposed relative to their
body mass (volume) → less heat is being dissipated.
Adult male polar bears
weigh between 550 to
1,200 pounds. Exceptionally
large individuals weigh as
much as 1,700 pounds.
Allen's rule (“A” = Appendages)
The long and narrow box (B) has the same volume but 1.75x greater
surface area exposed than the shorter and compacted box (A). The
greater the surface area exposed (box B) → the faster body heat will be
lost to the environment.
A and B have same volume.
B has 1.75 times greater
surface area.
A
B
A
Surface Area = 96
Volume = 64
Surface to Volume
Ratio = 1.5:1
B
Surface Area = 112
Volume = 64
Surface to Volume
Ratio = 1.75:1
Allen's rule (“A” = Appendages)
• In 1877, the American biologist Joel Allen observed that the length of
arms, legs, and other appendages also has an effect on the amount of
heat lost to the surrounding environment.
• Among endothermic animals, individuals in populations of the same
species living in warm climates near the equator tend to have longer
limbs than do populations living further away from the equator in
colder environments.
• A body with relatively long appendages → is less compact and → has
more surface area exposed.
• The greater the surface area exposed → the faster body heat will be
lost to the environment.
• http://anthro.palomar.edu/adapt/adapt_2.htm
Hot versus Cold Climates
• You are measuring the average weight, ear
lengths, and leg lengths of two populations of
coyotes; one in Alaska and one in Joshua Tree
National Park (desert).
Hot versus Cold Climates
• You are measuring the average weight, ear
lengths, and leg lengths of two populations of
coyotes; one in Alaska and one in Joshua Tree
National Park (desert).
• Which population would you expect to have a
higher average weight?
• Which population will have an average longer ear
length?
• Which population will have an average shorter
leg length?
Surface to Volume Ratios
• What is the advantage of having a smaller
body size in the desert?
– Hint: Do you want to retain heat or lose heat on a
hot day in the desert?
Why are cells so small?
Cell # 1
Cell #2
1. Which cell has a greater surface area exposed in proportion to volume?
2. Which cell will be able to get more oxygen across its cell membrane in
proportion to volume? (The cell needs to get oxygen from the environment
across the cell membrane to the mitochondrion to make ATP)
Surface to Volume Ratios
SMALLER CELLS HAVE MORE SURFACE AREA EXPOSED IN PROPORTION
→
TO VOLUME than large cells
smaller cells are more efficient at
transporting material across their cell membrane
The Smaller the object,
the Larger the SURFACE AREA EXPOSED PER UNIT OF VOLUME → more
efficient to exchange its internal content with the environment
Mouse to Elephant Curve
• Why would you expect a
mouse to have a higher
metabolic rate per unit
body weight than an
elephant?
• Which would you have to
feed more per unit body
weight, a mouse or an
elephant?
Kit foxes are the smallest foxes in North America. They have
exceptionally long ears, a slender body, long legs, and a long tail.
What habitat in California would you expect this fox to be found in?
• Does the body plan of the
kit fox follow the principles
of Bergmann’s and Allen’s
rule? Explain.
• Average weight is
3.5 to 7 pounds
• Large ears: 2.8 –
3.75 inches
• Body without tail:
18 – 21 inches
• Tail: 9.85 – 13.4
inches