1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Calculus - Word Problems

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data

    A spherical balloon is being inflated at the rate of 10 cu in/sec. Find the rate of change of the area when the balloon has a radius of 6 in.

    2. Relevant equations

    [tex] V = \frac {4}{3} \pi r^{3} [/tex] and [tex] A = 4 \pi r^{2} [/tex]

    3. The attempt at a solution

    [tex] \frac {dV}{dt} = \frac{4}{3} \pi 3r^{2}\frac{dr}{dt} [/tex]

    [tex] \frac {dA}{dt} = 4 \pi 2r\frac{dr}{dt} [/tex]

    the value of dV/dt is given in the question so

    [tex] \frac {dV}{dt} = 10 in^{3}/sec [/tex]

    If we substitute the value into the volume equation we can find dr/dt like so

    [tex] 10 = \frac {4}{3} \pi 3r^{2}\frac{dr}{dt} [/tex]

    [tex] \frac {10}{\frac {4}{3} \pi 3r^{2}} = \frac {dr}{dt} [/tex]

    then set r = 6 we get

    [tex] \frac {dr}{dt} = \frac {10}{452.39} = .0221 [/tex]

    Then move on to solve this equation for dA/dt

    [tex] \frac {dA}{dt} = 4 \pi 2r\frac{dr}{dt} [/tex]

    substituting dr/dt value from other equation and setting r = 6 again

    [tex] \frac {dA}{dt} = 10/3 ~= 3.33 in^{2}/sec [/tex]

    Word, problem solved
    Last edited: Apr 14, 2010
  2. jcsd
  3. Apr 14, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Second line. dV/dt=(4/3)*pi*(3*r^2*dr/dt). The r is squared.
  4. Apr 14, 2010 #3
    oh yeah it totally is!
  5. Apr 14, 2010 #4
    Yeah that was all, thanks man, totally solved. if you could take a look at the other one, I think that I have solved the cone problem as much as I could.. either way though, thanks
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Differential Calculus - Word Problems