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Numerade Educator

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Problem 33 Medium Difficulty

The edge of a cube was found to be $ 30 cm $ with a possible error in measurement of $ 0.1 cm. $ Use differentials to estimate the maximum possible error, relative, error, and percentage error in computing (a) the volume of the cube and
(b) the surface area of the cube.

Answer

(a) $270,0.01,1 \%$
(b) $36,0.0067,0.6 \%$

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Video Transcript

We know that if we are vey Alexis X Cube than Devi over DX In other words, the derivative is gonna be three x squared. Therefore, we know three X squared times Delta acts is Delta V. Therefore we know relative errors error over the volume. So to 70 we got this by doing three times 30 squared times 0.1 over 30 cubed 0.1 0.1 The relative air times 100 gives us 1% is the maximum errors to 70 centimeters cubed relative a rose 0.1 and percentage error as a percent would be 1%.