Related Rates: Introduction + Balloon Problem

in hive-128780 •  5 days ago  (edited)

In this video I go over a brief introduction on related rates and then solve an example inflating a spherical balloon to help further illustrate the basic concepts of related rates.


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Related Rates: Intro + Balloon Example

Related Rates  Intro  Balloon Example.jpeg

Introduction

  • If we are pumping air into a balloon both the volume and the radius are increasing and their rates of increase are related to each other.
  • But it is much easier to measure directly the rate of increase of the volume than the rate of increase of the radius.
    • This is because we can easily pump a known volume of air, for example, without worrying about the geometry (which we would need if measuring the radius)
  • In a related rates problem the idea is to compute the rate of change of one quantity in terms of the rate of change of another quantity (which may be more easily measured).
  • The procedure is to find an equation that relates the two quantities and then use the Chain Rule to differentiate both sides with respect to time.

Example

Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm3/s. How fast is the radius of the balloon increasing when the diameter is 50 cm?

Solution

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