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.
1 answer:
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
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