What are the dimensions of intensity?

[Old Guy]

Homework Statement

I know that intensity is power per unit area. When I do a dimensional analysis, it reduces down to mass per cubic time. Is there any physical significance to that?

Homework Equations

I=P/A

The Attempt at a Solution

 

[lightgrav]

Not really, because that form has removed all the geometry of the situation;
Intensity's geometry comes from the energy flow vector piercing an Area, so a flow Volume is indicated.
On the other hand, if you divide the intensity by flow velocity, you end with m v^2 / length^3 ;
light's intensity divided by light speed leaves you with mc^2 / volume, the energy density in the light.