# What are the dimensional units of A and B if a volume, V, is given by the equation V=A*t^3+B/t?

Mar 19, 2016

$A$ is ${L}^{3} / {T}^{3}$ and $B$ is ${L}^{3} \cdot T$

#### Explanation:

Any volume can be expressed as cubic length, ${L}^{3}$

Only adding up cubic lengths on the right will give the result of another cubic length on the left (Note: multiplying terms would not do this).

So, given $V = A \cdot {T}^{3} + \frac{B}{T}$, let

$A \cdot {T}^{3} = {L}^{3}$ meaning the first term is a volume (cubic length), and
$\frac{B}{T} = {L}^{3}$ meaning the second term is also a volume.

Finally we just solve for the respective letters, $A$ and $B$.

$A = {L}^{3} / {T}^{3}$
$B = {L}^{3} \cdot T$