Related Rates and Volume and Change in height

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SUMMARY

The discussion focuses on solving related rates problems involving the volume of a cone, specifically using the formula V = (1/3)πr²h. The participant assumes that the rate of change of height (dh/dt) is 0.2 ft/min and applies the chain rule for differentiation to find the relationship between the radius and height. The solution process involves substituting height for radius to simplify calculations, avoiding multi-variable calculus. The final arithmetic step was not verified, but the participant expresses confidence in the preceding calculations.

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  • Understanding of related rates in calculus
  • Familiarity with the volume formula for cones
  • Knowledge of differentiation and the chain rule
  • Basic arithmetic skills for verifying calculations
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  • Explore more complex volume-related calculus problems
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Students studying calculus, particularly those focusing on related rates and volume calculations, as well as educators seeking to enhance their teaching methods in these topics.

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Homework Statement


http://i6.minus.com/jErr8PMddiofz.png


Homework Equations



V of cone = pi/3 (r^2)h

The Attempt at a Solution



I'm assuming this is correct and that dh/dt = 0.2 ft/min

I basically substituted a value of h in for the radius so I wouldn't be doing multi-var calculus and differentiated from there using the chain rule as needed.

http://i.minus.com/jUeLLF0Kxg3hp.jpg
 
Last edited by a moderator:
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I didn't check the arithmetic in the final step, but it looks fine down to there.
 
Alright great :-)! Thanks ::)
 

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