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

Mar 25, 2016

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 $25.0 {\text{ m}}^{2}$ and have an unknown height of $x \text{ meters}$. So we need to solve the volume of this box as

$V = \text{area"xx"height"=25" m"^2*x " m}$

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

$1 {\text{ gal" = 3.78xx10^-3 " m}}^{3}$

So,

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

$x = 1.512 \times {10}^{-} 4 \text{ m" = 0.1512 " mm}$