Answer:
The approximate amount of paint required for the job is [tex]94.08 \: cm^3[/tex].
Step-by-step explanation:
Given a function y = f(x) we call dy and dx differentials and the relationship between them is given by,
dy = f′(x)dx
Let s be the edge of the cube.
The volume of a cube is given by
[tex]V=s^3[/tex]
The amount of paint needed is
[tex]\Delta V \approx dV[/tex]
Differentiating, we get:
[tex]dV=3s^2ds[/tex]
When [tex]s=28[/tex] and the thickness is [tex]ds=0.04[/tex], this becomes
[tex]dV=3(28)^2(0.04)\\dV=94.08 \: cm^3[/tex]
The approximate amount of paint required for the job is [tex]94.08 \: cm^3[/tex].
