Size matters I
Bill Indge
Size matters
How science
works
Knowledge and
understanding
Application and analysis
Size matters
Analysis and
interpretation
Knowledge and
understanding
Application of knowledge and understanding
Size matters
Size and surface area to volume ratio
1 cm
Surface area = 1×1×6 = 6 cm2
Volume = 1×1×1 = 1 cm3
1 cm
Surface area = 6 = 6
Volume
1
1 cm
Size matters
6
5
Surface area
to volume
ratio
4
3
2
1
0
0
1
2
3
4
Side length
5
6
Size matters
6
Surface area
to volume
ratio
5
Small organisms have a
large surface area to
volume ratio
4
3
2
1
Large organisms have
a small surface area to
volume ratio
0
0
1
2
3
4
Side length
5
6
Size matters
The formula for finding the surface area of a sphere is 4πr2.
The formula for finding the volume of a sphere is (4/3) × πr3.
(a) Explain how the surface area to volume ratio of a sphere
may be calculated from the expression:
surface area to volume ratio = 3/r (3 marks)
Size matters
Answer: (a) The surface area to volume ratio of a sphere is
calculated by dividing the surface area by its volume:
4πr2
(4/3) × πr3
Simplify by cancelling, in other words, dividing the top line and
the bottom line by 4, π and r2. This gives:
1
(1/3)r
Multiplying the top and the bottom lines by 3 gives:
3/r
(3)
Size matters
(b) Use this simplified expression to complete the table.
(1 mark)
Radius of sphere
1
2
3
4
5
6
Surface area to
volume ratio
3.0
0.5
Size matters
Answer (b)
(1)
Radius of sphere
1
2
3
4
5
6
Surface area to
volume ratio
3.0
1.5
1.0
0.8
0.6
0.5
(c) Assume that a cell is spherical. Use the data in the table
to describe the relationship between the size of a cell and its
surface area to volume ratio.
(1 mark)
Size matters
Read the information in the
stem. You will need this to
answer the question.
Seals
The southern elephant seal is
a very large mammal. Fully
grown male elephant seals
may reach a length of almost
5 m and have a mean body
mass of 3200 kg. Elephant
seals spend much of their
lives in the cold waters around
the sub-Antarctic islands.
Size matters
Explain the advantage of a large size to a mammal that lives
in cold water. (3 marks)
• Seals are mammals and have a high body temperature;
• Will lose less heat to the surrounding water;
• Because they have a small surface area to volume ratio; (3)
Size matters
Again start by reading the
information in the stem. You
will need this.
Earthworms
Many species of earthworms
burrow through the soil.
Earthworms of one particular
species may be up to 200 mm
in length although their
diameter is only 6 mm.
(a) Explain the advantage to an
earthworm of being covered in
mucus.
(2 marks)
Answer (a)
• Acts as a lubricant;
• Enables the worm to move
easily through the soil when
burrowing; (2)
Size matters
(b) The oxygen that earthworms require for respiration diffuses
through their body surface into the blood vessels in the skin.
Explain how the shape of a burrowing earthworm aids diffusion.
(2 marks)
Answer (b)
• The rate of diffusion is directly proportional to surface area;
• Earthworm has large surface area to volume ratio; (2)
(c) In dry conditions, soil-dwelling earthworms curl into a ball.
Explain the advantage of this behaviour to an earthworm in dry
conditions.
(2 marks)
Answer (c)
• Provides a smaller surface area to volume ratio;
• From which to lose water/for evaporation; (2)
Size matters
Elephants
Signposts
• Where questions are based
on a passage, start by
reading it through quickly.
• Underline one or two words
in each paragraph. These
words should indicate what
the passage is about and
will help you to find your
way around.
Size matters
Signposts
African elephants are the largest of all land
mammals. Although geographically
variable in size, fully mature males average
over 3 m at the shoulder and have a mean
body mass of around 5000 kg. Mature
females are smaller and have
corresponding measurements of 2.5 m and
3000 kg. Elephants formerly occurred
throughout sub-Saharan Africa, wherever
water and trees were found.
Size matters
Signposts
•
•
•
•
African elephants – size
Ear flapping
Thermal windows
Dust bathing
This should enable you to find your way
round the passage and locate the
information you want quickly.
You can then read the paragraph you
want more carefully, when you want it.
Size matters
(a) The features of the blood vessels in the ears of an elephant
described in the passage could result in heat loss (lines 8–9).
Explain how. (3 marks)
Answer (a)
• Dense capillary bed provides large surface area;
• Large diameter of arteries ensures delivery of large volume
of blood;
• Blood at core temperature/at higher temperature than that
of the environment.
(3)
Size matters
(b) If ear flapping plays an important role in heat loss, explain
why you would expect its frequency to:
(i) increase as the ambient temperature rose (lines 10–11)
(2 marks)
(ii) be inversely related to wind velocity (lines 11–12)
(2
marks)
Answer (b) (i)
• Flapping will increase airflow over the ears/will increase heat
loss by convection;
• Temperature gradient between body surface and surroundings
lower/less heat can be lost to surroundings from body surface;
(2)
Answer (b) (ii)
• As wind speed/velocity increases, more heat is lost;
• Ear flapping requires expenditure of energy by the elephant;
(2)
Size matters
(c) Explain what is meant by a ‘thermal window’ (line 14).
(3 marks)
Answer (c)
• An area of increased blood flow;
• On skin/surface of animal;
• Associated with heat loss;
(3)
(d) Explain how ‘restriction of areas of enhanced blood flow to
thermal windows’ might enable an elephant to ‘react more
flexibly to its needs regarding heat loss’ (lines 16–18).
(2 marks)
Answer (d)
• The use of thermal windows allows heat loss from small
discrete areas;
• Which can be recruited independently;
• Allows finer control than from the whole body surface; (2)
Size matters
(e) The researchers investigating dust bathing concluded that
its function was not related to thermoregulation. Identify and
explain the evidence in the passage that supports this
conclusion.
(3 marks)
Answer (e)
• Frequency of dust bathing independent of body mass;
• Larger elephants have a smaller surface area to volume
ratio;
• Larger elephants generate more metabolic heat;
• Expect frequency to increase with body mass; (3)