# What is the surface area to volume ratio for a cube that measures 4 cm on each side?

Nov 19, 2015

$A = 96 c {m}^{2}$
$V = 64 c {m}^{3}$
$R a t i o = \frac{96 c {m}^{2}}{64 c {m}^{3}} = 1.5$

#### Explanation:

You calculate the total surface area by finding the area of a single side of the cube and then multiplying that area by six (for the six sides of a cube).

Once you do this you will find that a 4cm Cube has a total surface area of $96 c {m}^{2}$.

To find the volume you simply use the following formula:

${V}_{c u b e} = L \cdot W \cdot H$

In this case (because it is a cube) you will use 4cm for each value:

${V}_{c u b e} = 4 c m \cdot 4 c m \cdot 4 c m = 64 c {m}^{3}$

To find the ratio of surface area to volume, simply divide the surface area by the volume:

Ratio $= \frac{96 c {m}^{2}}{64 c {m}^{3}} = 1.5$

Ratios are generally unit-less as they are comparing two values rather than combining to form a new value.