 Surface
Area: The measure of how much
exposed area a solid object has, expressed in
square units (x2).
 Volume: How much three-dimensional space a
substance (solid, liquid, gas, or plasma) or shape
occupies and is expressed in cubed units (x3).
 Ratios (Surface Area:Volume) or Fractions
(SA/V) make comparisons between two things.
1. Out of these three, solid, 3D shapes, which has the biggest surface
area?
2. Which has the biggest volume?
3. Which has the biggest surface area to volume ratio?
4. Which of these animals has the biggest surface area to volume ratio?
A. Giraffe
B. Elephant
C. Horse
D. Hamster
E. Don’t know
5. How is the job of the mitochondria improved by having an inner
membrane with many folds?
What shape does your
body take when you
are hot?
What shape does your
body take when you are
cold?
Why are the shapes of these
rabbits’ ears so different?
Which has the higher SA:V ratio?
Why?
Do these plants have low or high
SA:V ratios?
Why do they have this shape?
If SA increases will V increase?
 If SA decreases will V decrease?

Will the increase or decrease
be at the same rate?
Talk to your neighbor about your answers and
write your hypotheses on your worksheet in a full sentence.
(for example: As surface area increases volume will…)
Equations for Surface Area:
Equations for Volume:
Rectangle: 2(wh) + 2(lw) + 2(lh)
Rectangle: lwh
Cube: 6x2
Cube: x3
A.
B.
C.
A.
B.
= 112 units2
Volume = 8*2*4 = 64 units3
= 136 units2
= 96 units2
Volume = 43 = 64 units3 Volume = 2*2*16 = 64 units3
C.
Surface Area = 2(2*4 + 8*2 + 8*4) Surface Area = 6*42 Surface Area = 2(2*16 + 2*2 + 2*16)
Cube with increasing size
Sphere with increasing
radius
cm^2 or cm^3
1200
1000
5000
800
4000
600
SA (cm2)
400
Volume (cm3)
3000
2000
1000
200
0
0
2
3
4
5
6
7
8
length of side (cm)
9
10
2
3
4
5
6
7
8
9
10
radius
As size increases (as seen on the X axis) what happens to SA and V?
Do SA and V change at the same rate?
Which changes faster with increasing size?
What happens to the SA:V ratio as size increases?
How does this change your hypotheses?
Protists
Neuron Cell
SA:V ratios and size
Cube with increasing size
100%
90%
80%
70%
60%
50%
Volume (cm3)
40%
SA (cm2)
30%
20%
10%
0%
2
3
4
5
Size
6
7
8
9
At size 2 the SA:V ratio is 75:25 or 3:1
At size 3 the SA:V ratio is 66:33 or 2:1
At size 6 the SA:V ratio is 50:50 or 1:1
At size 9 the SA:V ratio is 40:60 or 2:3
At size 10 the SA:V ratio is 33:66 or 1:2
10
The SA:V ratio decreases with increasing size.