Acoat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of edge 28 cm. use differentials to find the approximate amount of paint (in cm3) required for the job, correct to the nearest cubic centimeter. hint: the volume of a cube of edge s is v = s3.

The approximate amount of paint required for the job is .

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

The amount of paint needed is

Differentiating, we get:

When and the thickness is , this becomes

The approximate amount of paint required for the job is .

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