A cube is measured and each side is found to be 18 inches with a possible error of at most 0.005 inches. What is the approximate error in computing the volume of the cube.

Expert Answers

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You need to come up with the following notation to the side of the cube such that:

x = side of cube

You need to remember the formula that gives the volume of the cube:

`V(x) = x^3`

You need to differentiate the function of volume with respect to x such that:

`(dV(x))/(dx) = (d(x^3))/(dx)`

`dV = 3x^2 dx`

The problem provides the information that the length of the side of cube is of 18 inches and the error is of 0.005 inches such that:

`dV = 3*18^2*0.005 = 4.86` 

Hence, evaluating the approximate error in computing the volume of the cube yields `dV = 4.86` .

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