# Investigating Surface Area/Volume ratio

2 4 6 8 12

Investigating Surface Area/Volume ratio Introductory Notes: Surface Area to Volume Ratio side of cube

20

Side 2 Area of side Total Area

2x2 4 6x2x2 24

Area of Cube's Surface

4x4 6x6 16 36 8x8 64 12x12 144 6x4x4 6x6x6 6x8x8 96 216 384 6x12x12 864 20x20 400 6x20x20 2400

Side 3

2x2x2 4x4x4 6x6x6 8x8x8 8

Volume Ratio of Surface Area to Volume 3:1

64 216 512 12x12x12 1728 20x20x20 8000

3:2 3:3 3:4 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,