Question

If a gallon of paint covers a `25.0 " m"^2` wall, what is the thickness of the paint?

Answer 1

The paint is 0.1512 millimeters thick.

Explanation:

If, instead of painting a wall, let's suppose we are pouring the paint into a box. We know the surface of the "floor" of this box would be `25.0 " m"^2` and have an unknown height of `x " meters"`. So we need to solve the volume of this box as

`V="area"xx"height"=25" m"^2*x " m"`

Now, we were given a gallon of paint. Google told me that

`1 " gal" = 3.78xx10^-3 " m"^3`

So,

`V=25 " m"^2*x " m"=3.78xx10^-3 " m"^3`, dividing both sides by 25 gives the "height" (or thickness), `x`,

`x=1.512xx10^-4 " m" = 0.1512 " mm"`