February 20th, 2011, 08:57 PM  #1 
Newbie Joined: Feb 2011 Posts: 6 Thanks: 0  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. 
February 20th, 2011, 09:29 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  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.

February 20th, 2011, 09:49 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Derivatives: Differentials
I recommend also comparing dV to ?V (both cases) to verify this is a good approximation.


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