# Calc04_6 - 4.6 Related Rates Olympic National Park...

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Olympic National Park, Washington Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007 4.6: Related Rates

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Olympic National Park, Washington Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007 4.6: Related Rates
Olympic National Park, Washington Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007 4.6: Related Rates

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First, a review problem: Consider a sphere of radius 10cm. If the radius changes 0.1cm (a very small amount) how much does the volume change? 3 4 3 V r π = 2 4 dV r dr = ( 29 2 4 10cm 0.1cm dV = 3 40 cm dV = The volume would change by approximately . 3 40 cm
instantaneous rate of 0.1 cm/sec. (Possible if the sphere is a soap bubble or a balloon.) 3 4 3 V r π = 2 4 dV dr r dt dt = ( 29 2 cm 4 10cm 0.1 sec dV dt = 3 cm 40 sec dV dt = Note: This is an exact answer, not an approximation like we got with the differential problems.

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## This note was uploaded on 02/11/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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Calc04_6 - 4.6 Related Rates Olympic National Park...

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