Q:

Using differentials, estimate the amount of paint need to apply a coat of paint 2mm thick to a sphere with a radius of 30cm.

So first I use the surface area of a sphere which is $$ SA=4\pi r^2$$
but after that I have no idea what to do next because I shouldn't apply $\frac{d}{dx}$ until I have substituted in something for $r$ right?

A:

$V = 4/3×\pi r^3$
$dV/dr = 4\pi r^2$
Lower estimate for paint volume is 
$dV = 4\pi r^2 dr$ 
dr = 2mm, r = 30cm.  Calculate dV in cm$^3.$

