Students should be able to calculate and compare surface area to volume…

The idea

Surface area to volume ratio (SA:V) compares the total external surface area of an object with its volume. For a cube of side length L, surface area = 6 × L² and volume = L³, so SA:V = 6 ÷ L. As an organism or structure gets larger, volume increases faster than surface area, so the ratio falls. For example, a cube of side 1 cm has SA:V = 6 ÷ 1 = 6, while a cube of side 3 cm has SA:V = 6 ÷ 3 = 2. To calculate, work out surface area and volume using the correct formulae, then divide surface area by volume and cancel units. To compare, calculate the ratio for each object and state which is larger, linking this to how quickly substances can diffuse into or out of the object.

What earns the marks

• Calculate surface area correctly using the appropriate formula for the shape, such as 6 × L² for a cube.
• Calculate volume correctly using the appropriate formula, such as L³ for a cube.
• Divide surface area by volume to obtain the ratio, cancelling units correctly.
• Compare two or more ratios and state which object has the larger or smaller surface area to volume ratio.
• Relate a larger surface area to volume ratio to more effective diffusion over the available surface.

Common mistakes and how to put them right

• Dividing volume by surface area instead of surface area by volume.

  Put it right by writing the ratio as surface area first, then volume.

• Forgetting to square or cube the side length.

  Put it right by checking each formula before substituting numbers.

• Assuming the larger object always has the larger ratio.

  Put it right by calculating both ratios, since larger objects usually have a smaller ratio.

Exam tips

• Write the formula, substitute values, then give the final ratio with units cancelled.
• Show each step of working so method marks can be awarded even if the final value is wrong.
• When comparing, quote both calculated ratios and then make the comparative statement explicit.