### Video Transcript

A student is trying to remember
a formula from geometry. Assuming that π΄ corresponds to
area, π corresponds to volume, and all other variables are lengths. What missing dimension in the
formula π equals π΄ must the right-hand side of the equation be multiplied by
to make the formula dimensionally consistent?

Considering these two terms, π΄
corresponding to area and π to volume, if we write out their dimensions, the
dimensions of π΄ are length squared, while the dimensions of π are length
cubed. Considering the formula π
equals π΄ multiplied by something, weβre asked what dimension needs to fit in to
that blank spot. If we look at the equation from
a dimension perspective, we can see that, on the left-hand side, we have πΏ
cubed. And currently, on the
right-hand side, we have πΏ squared. So weβre missing a dimension of
πΏ.

This means we would want to
multiply the right-hand side of our equation by a length πΏ in order to make it
dimensionally consistent. And with this πΏ in place, our
equation is.