Maths for A Level Biology - updated edition

across the average distance between collisions, after which they may be sent in different directions. Consequently, if a molecule is required to travel a distance greater than the distance between collisions, its movement will not be efϐicient. Collisions will keep changing its direction. Organisms using diffusion must either transport over very small distances only or have a large surface area to compensate for the inefϐiciency. Single cells rely on diffusion for absorption and transport but mammals need the large surface areas of lungs and the ileum to provide enough area that the diffusion across them is adequate. They also need a transport system to move molecules around the body. An aspect of this that may be tested in Biology courses examines the surface area : volume ratio of cells or whole organisms where they may be simpliϐied to a geometric shape, such as a cube, a sphere or a cylinder. You may be expected to calculate areas, volumes or their ratios. You would not be expected to remember the equations for the surface area or volume of a sphere. Organisms as cubes You may be asked to do similar calculations thinking of organisms as cubes. In this case, you would be expected to remember how to calculate the area and volume. The table below shows you how to do the calculation for two imaginary animals, one with sides of 1 unit and one with sides of 2 units. It doesn’t matter what the units are for this argument, because you are ϐinding a ratio. It might help to think about approximately cubic organisms, like a toad or a rhinoceros, as long as you ignore the limbs. 1 1 1 2 2 2 Length of each side 1 2 Area of each face 1 × 1 = 1 2 × 2 = 4 Number of faces 6 6 Total area 6 × 1 = 6 6 × 4 = 24 Volume 1 × 1 × 1 = 1 2 × 2 × 2 = 8 Surface area : volume ratio 6 : 1 24 : 8 = 3 : 1 The biological meaning of this is that for an organism of one unit length, for each unit of volume, there are 6 units of area. But if the organism has 2 units length for its dimensions, then each unit of volume has only 3 units of area. In other words, the bigger the organism, the less surface area it has for each unit of volume. This means that the bigger it is, the less likely diffusion alone can provide all the food and oxygen needed and remove all the carbon dioxide. Pointer Organisms can be thought of as geometric shapes such as cubes, spheres and cylinders, in order to make calculations about their area and volume. QUICKFIRE 2.4 Calculate the surface area : volume ratio of an organism simplified to a cube, with sides of 3 units. Pointer Diffusion is only efficient over small distances. Mathematics for Biology 36