Question

A coat 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.

Answer 1

The approximate amount of paint required for the job is
`94.08 \: cm^3`.

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

`V=s^3`

The amount of paint needed is

`\Delta V \approx dV`

Differentiating, we get:

`dV=3s^2ds`

When
`s=28` and the thickness is
`ds=0.04`, this becomes

`dV=3(28)^2(0.04)\\dV=94.08 \: cm^3`

The approximate amount of paint required for the job is
`94.08 \: cm^3`.