side of cube
2
4
6
8
12
Investigating Surface Area/Volume ratio
Introductory Notes:
Surface Area to Volume Ratio
20
Side 2
Area of side
2x2 4
Total
Area
6x2x2 24
Area of
Cube's
Surface
4x4 16
6x6 36
6x4x4 96
6x6x6 216
8x8 64 6x8x8 384
12x12 144 6x12x12 864
20x20 400 6x20x20 2400
Side 3 Volume
Ratio of Surface
Area to
Volume
3:1 2x2x2 8
4x4x4 64
6x6x6 216
8x8x8 512
12x12x12 1728
3:2
3:3
3:4
20x20x20 8000
3:6
3:10
So, if we double the side the area goes up by FOUR times ( 2 2 )
But the volume goes up by a factor of EIGHT times ( 2 3 )

So the ratio of surface area to volume is lower in a large animal than a smaller one.
Since heat is transferred at the surface, a small animal has greater potential for rapidly gaining and losing heat than a larger one because of its relatively large surface area.
A smaller animal also has greater relative potential for evaporative water loss through its greater area of skin.
Ground Squirrels have a LARGE Surface Area/Volume Ratio
They lose and gain heat rapidly. They live in burrows to keep them selves cool in the Summer heat, and warm in winter. The water requirements of the squirrel are supplied mainly by the food they eat.
(Photo taken in Arizona …in the shade …when the temperature was 110 C )

A polar Bear]
POLAR BEARS have a SMALL Surface Area/Volume Ratio
This helps it to survive in cold climates. This image was taken on a hot day
(San Diego Zoo) so it was obviously finding it difficult to keep cool! It used the cool water to increase the heat loss.
The jackrabbit has a large ears to increase its surface area to volume ratio
This jackrabbit is really struggling to keep cool in Arizona. It is sheltering from the intense heat, in shade. The large ears, with an extensive area of blood vessels, help it dissipate as much heat as possible.

Investigating Surface Area/Volume
In this investigation we will place equal volumes of hot water in different size beakers. This provides different surface areas….but the same volume
Procedure:
Obtain at least TWO different size beakers.
Place a given volume of hot water in one beaker.
Take the initial temperature of the water
Take the temperature of the water after 10 minutes
Calculate the surface area of the water
Repeat, using a different size beaker, and the same volume of water.
You only have to calculate the surface area. You measure the volume with a measuring cylinder (or beaker)

Results Table
Design …….your table.
You need at least TWO sets of results (different surface areas)
Quantities required:
Volume
Surface Area
Surface Area/Volume
Initial Temperature
Final Temperature
Temperature Drop
Units should be in each table,