Maths for A Level Biology - updated edition

2 Volume and length of side 0 2 4 6 8 10 1000 800 600 400 200 0 Length of side Volume × × × × × ××××× This graph shows how volume increases as the length of the sides increases. As with the length, the increase is gradual with short lengths but becomes steeper as the length increases. 3 Surface area : volume ratio and length of side 0 2 4 6 8 10 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0 Length of side Surface area : volume ratio × × × × ×× × × × × This graph shows how the ratio of surface area : volume changes as the length of the sides gets longer. The ratio goes down, as could be seen from the calculations for cubes of sides 1 and 2 above. As the sides get longer, the ratio decreases less and less, so that above about 10 units, the ratio does not change very much. This graph says that the bigger the organism, the less surface area it has for every unit of its volume. But above a certain size, increase in size does not make much difference to the surface area : volume ratio. There are presumably other factors that limit the organism’s size, such as limb strength, speed of nervous impulse or ability to produce blood pressure that is high enough. A graph like this allows you to estimate the surface area : volume ratio for any length side, without having to calculate. For example, if you were asked to use the graph to estimate the surface area : volume ratio for an organism with sides of 1.5 units, drawing on the graph as shown, gives a ratio of 4.4 : 1. You might be asked to relate the ratios for these imaginary animals to their habitats. You would be expected to explain that those that have a larger surface area : volume ratio are better adapted for absorbing materials, such as glucose, minerals or oxygen, across their surface and better adapted for releasing materials such as carbon dioxide or ammonia across the surface. You might suggest that these smaller organisms could be aquatic, because if they rely purely on diffusion, the greater efϐiciency of movement in water than in air makes them more likely to be adapted to living in water. Pointer Surface area : volume ratio gets smaller as organisms get bigger. QUICKFIRE 2.5 a) Estimate from the graph the surface area : volume ratio of a cube of side length 2.5. b) Check your estimate by calculating the correct answer. Pointer Always draw on the graph, rather than estimating by eye. You are more likely to be accurate. Mathematics for Biology 38