How Quickly Does the Radius of a Lollipop Decrease as You Eat It?

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Discussion Overview

The discussion revolves around a problem involving the rate of change of the radius of a spherical lollipop as it decreases in volume over time. Participants are exploring the mathematical approach to derive the relationship between the volume and the radius, specifically in the context of a lollipop losing volume at a constant rate.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a problem involving a spherical lollipop losing volume at a rate of 0.08 mL/min and seeks help in determining how fast the radius decreases when the lollipop is 20 mm across.
  • Another participant suggests that the derivative with respect to time should be taken to find \(\frac{dr}{dt}\).
  • A participant requests to see the derivative calculation to identify where the original poster might be confused.
  • It is mentioned that the chain rule should be applied, indicating that \(dV/dt = (dV/dr) (dr/dt)\) is necessary for solving the problem.

Areas of Agreement / Disagreement

Participants appear to agree on the need to differentiate the volume with respect to time and apply the chain rule, but there is no consensus on the specific steps or calculations involved, as some participants express confusion about the process.

Contextual Notes

There are indications of missing steps in the differentiation process, and the discussion does not resolve the specific calculations needed to find \(\frac{dr}{dt}\).

dmitridj
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Hey, I am having some trouble solving this problem..soon as i see how it works i just know i gunna go "Ooh, that's all i had to do" Here it is:

A shrinking lollipop. A shperical Tootsie Roll Pop that you are enjoying is giving up volume at a steady rate of 0.08 mL/min. How fast will the radius be decreasing when the Tootsie Roll Pop is 20 mm across?

Ok, I know I need to take the derivative of V=(4/3)pi(r^3) i just get lost in that process...please help..

THank you very much
 
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They are asking you for [tex]\frac{dr}{dt}[/tex]

Why don't you differiantiate with respect to t?.
 
dmitridj said:
Ok, I know I need to take the derivative of V=(4/3)pi(r^3) i just get lost in that process...please help..

Show me your derivative, so i can see where it went wrong.
 
you need to use the chain rule, dV/dt = (dV/dr) (dr/dt)
 

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