Question

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

Answer 1

`A` is `L^3/T^3` and `B` is `L^3*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*T^3+B/T`, let

`A*T^3=L^3` meaning the first term is a volume (cubic length), and
`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*T`