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Simple function question (Function to represent radius)

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data

    Ok here is the question, and I will give the answer below. I am not really clear on how the instructor got this answer. So, if anyone could explain the answer a little, I would REALLY appreciate it!

    Question: A spherical balloon with radius r centimeters has volume given by the formula V(r) = 4/3 pi r^3

    Find a function that represents the amount of air required to inflate the balloon from a radius of r centimeters to a radius of r + 1 centimeters.

    ANSWER: f(r) = 4/3 pi (r+1)^3 -4/3 pi r^3 = 4/3 pi (3r^2 + 3r + 1)

    I am not sure why and how this is the answer. ?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 10, 2011 #2
    Alright...
    You know that the amount of air (volume units) in a balloon with radius r is given by the formula for the volume you've written, that is, V1 = [itex]\frac{4}{3}\pi r^{3}[/itex].
    Now, the volume (=the volume the air would take) of a balloon with radius r+1 is given by the same formula, only r+1 instead of r: V2 = [itex]\frac{4}{3}\pi (r+1)^{3}[/itex].

    What is then the difference between the two quantities? Well, for that you have to calculate the difference surprisingly!

    Diff_V = V2 - V1

    And that's what you've written.
     
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