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Unformatted text preview: 92.131 Lecture 22 1 of 11 Ronald Brent 2009 All rights reserved. Related Rates: Consider the following problem: The mechanics at a Toyota Automotive are reboring a 6in deep cylinder to fit a new piston. The machine they are using increases the cylinders radius one thousandth of an inch every 3 minutes. How rapidly is the cylinder volume increasing when the bores radius is 3.800 in.? Step 1: Picture and Variables Let V = volume (in 3 ) of the bore at time t (min) r = radius (in) of the bore at time t . Step 2: Numerical Information: r = 3.800 in and 3000 1 = t d r d in/min 6 in r 92.131 Lecture 22 2 of 11 Ronald Brent 2009 All rights reserved. Step 3: What do we want to find ? Ans: t d V d Step 4: How are the variables related? The cylinders volume is: 6 ) ( 2 r V = Step 5: Differentiate with respect to t . t d r d r t d V d 12 = Step 6: Evaluate : 3000 1 800 . 3 12 = t d V d so 0478 . 250 8 . 3 = t d V d in 3 /min 92.131 Lecture 22 3 of 11 Ronald Brent 2009 All rights reserved. The method for solving relatedrate problems is as follows: 1. First draw a picture labeling all appropriate variables. Use t for time....
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 Fall '09
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 Calculus

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