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A coat of paint of thickness 0.06 cm is to be applied uniformly to the faces of a cube of edge 33 cm. Use differentials to find the approximate amount of paint required for the job, correct to the nearest cubic centimeter.

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Answer:

392 cm^3

Step-by-step explanation:

Let X represent the edge of a cube

let t represent the thickness of the paint.

Volume of a cube = x^3

V = x^3

Differentiate V with respect to x

dV/dx = 3x^2

dV = 3x^2 dx

dx = 2dt

= 2(0.06)

= 0.12

dV = 3(33)^2 (0.12)

dV = 392.04cm^3

dV = 392 cm^3