B1 M) Surface Area to Volume Ratio
How easy it is for organisms to exchange substances with their environments depends on the organism’s surface area to volume ratio. A larger surface area to volume ratio makes it easier for organisms to exchange substances. Smaller organisms have larger surface area to volume ratios than larger organisms.
Exam questions to do with surface area to volume ratios tend to focus on cubes. A cube is a 3D shape where all of the sides are the same length and all 6 of the faces are the same area. We are going to find the surface area to volume ratios for the two cubes below; one cube has sides that are 2 cm and the other cube has sides that are 3 cm.
Cube 1 has sides that are 2cm.
Cubes have 6 identical faces, so we find the total surface area of a cube by multiplying 6 by the area of one of the faces. We find the area of one of the faces by multiplying the length by the width, which gives us 4 cm2 (2 x 2). We then multiply by 6, which means that the total surface area is 24 cm2.
We find the volume of a cube by multiplying the length by the width by the height; all of these values are 2. The volume of the cube is 8 cm3.
So, for the 2 cm cube, the surface area is 24 cm2 and the volume is 8 cm3. This means that the surface area to volume ratio is:
Cube 2 – 3 cm
We now do the same process for the second cube, which has sides that are 3 cm.
We work out the total surface area by multiplying 6 by the area of one face, which tells us that the surface area is 54 cm2.
We find the volume of a cube by multiplying the length by the width by the height; all of these values are 3. The volume of the cube is 27 cm3.
So, for the 3 cm cube, the surface area is 54 cm2 and the volume is 27 cm3. This means that the surface area to volume ratio is:
We now simplify our ratio by dividing by common factors between the numbers in the ratio. 27 is a factor of 54 and 27, so we divide both of the numbers in the ratio by 27.
The simplified surface area to volume ratio is 2 : 1.
We can now compare the two ratios; the SA : Vol ratio for cube 1 (sides 2 cm) is 3 : 1, and the SA : Vol ratio for cube 2 (sides 3 cm) is 2 : 1. The SA : Vol ratio for cube 1 is greater than it is for cube 2. So, the smaller cube has a larger surface area to volume ratio than the larger cube. Therefore, smaller organisms have larger surface area to volume ratios compared to larger organisms.