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February 20th, 2011, 08:57 PM   #1
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Derivatives: Differentials

In a manufacturing process, ball bearings must be made with radius of 0.4 mm, with a maximum error in the radius of 0.015 mm. Estimate the maximum error in the volume of the ball bearing.

Solution: The formula for the volume of the sphere is ______. If an error ?r is made in measuring the radius of the sphere, the maximum error in the volume is ?V__= ________.

Rather than calculating ?V, approximate ?V with dV, where dV= _______.

Replacing r with ______ and dr=?r with _____ gives dV= _____
The maximum error in the volume is about ______ mm^3.
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February 20th, 2011, 09:29 PM   #2
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Re: Derivatives: Differentials

Start by looking up the formula for the volume of a sphere. Work out the volume given r=0.4, then try r=0.415 and r=0.385.
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February 20th, 2011, 09:49 PM   #3
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Re: Derivatives: Differentials

I recommend also comparing dV to ?V (both cases) to verify this is a good approximation.
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