Surface Area to Volume Ratios Haileybury Astana IB Biology

Why cells are small ? The size of a cell is limited by its need to exchange materials with its environment. The rate of metabolism of a cell increases with its volume. However, the rate of exchange of materials and energy (heat) is a function of its surface area.

Assume we have 3 cubes: 3 With sizes: 2 1 1 cm 10 cm 100 cm What will happen to ratio between Volume and Surface area as their size increases?

Ratio of V:S.A. Cube Side Length Volume (x3) S.A. (6x2) Ratio (S.A./V) 1 1 cm 2 10 cm 3 100 cm 1 cm3 6 cm2 6 0.6 1 000 cm3 600 cm2 1 000 000 cm3 0.06 60 000 cm2

Why are we made up of cells? 1. What is the surface area : volume ratio (SA:V) of a single cube of dimensions 10 x 10 x 10 cm? SA = V= SA:V= 2. What is the SA:V of 1000 cubes each with the dimensions 1 x1 x 1 cm? 3. Make a statement about the volumes and areas of the two situations above. 4. Why are living things made up of cells?

Why are we made up of cells? Each cell is closely associated with one or more capillaries which provide glucose and oxygen as well as removing carbon dioxide.

How does shape effect the SA : V? Consider a fixed volume of 64cm3. Produce scale drawings for the following: 4 x 4 x 4 cm 64 x x1 x 1 cm 8 x 8 x 1 cm 16 x 2 x 2 cm Determine the SA : V for each shape. Suggest an organism or a biological structure that the shape could represent

Questions Why are polar bears the largest bears in the world? Why do African Elephants have such large ears? Why do annelids only reach a certain size? Why do large living things have lungs or gills?

Going multicellular Under a certain ratio (S.A./V), cells cannot get bigger, they can only get more numerous