Results 1 to 5 of 5

Math Help - Related Rates Questions

  1. #1
    a.a
    a.a is offline
    Junior Member
    Joined
    Mar 2008
    Posts
    67

    Exclamation Related Rates Questions

    A spherical ballon is being inflated at a rate of 3 pi m^3/min. Twelve minutes after inflation first begins, what is the rate of increase of the diameter?

    i solved for dr/dt and then adjuster for diameter, but i dont understand why we were given t = 12 min...

    thx for any help u can giv
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by a.a View Post
    A spherical ballon is being inflated at a rate of 3 pi m^3/min. Twelve minutes after inflation first begins, what is the rate of increase of the diameter?

    i solved for dr/dt and then adjuster for diameter, but i dont understand why we were given t = 12 min...

    thx for any help u can giv
    Let diameter be D. Then \frac{dD}{dt} = \frac{dD}{dV} \times \frac{dV}{dt}.


    Given: \frac{dV}{dt} = 3 \pi \, m^3/min.

    Common knowledge: V = \frac{4}{3} \, \pi r^3 = \frac{\pi}{6} \, D^3. Therefore \frac{dV}{dD} = \frac{\pi}{2} \, D^2.

    Therefore: \frac{dD}{dt} = \frac{2}{\pi D^2} \times 3 \pi = \frac{6}{D^2}.


    You were given t = 12 minutes because that's the question!!! Find the value of  \frac{dD}{dt} when t = 12 minutes!

    So you have to substitute the value of D at t = 12. Clearly V = (12)(3 \pi) = 36 \pi \, m^3 and you know that V = \frac{\pi}{6} \, D^3. Therefore D = ....... at t = 12 minutes.

    Therefore  \frac{dD}{dt} when t = 12 minutes is equal to ......
    Follow Math Help Forum on Facebook and Google+

  3. #3
    a.a
    a.a is offline
    Junior Member
    Joined
    Mar 2008
    Posts
    67
    Thx a million.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    a.a
    a.a is offline
    Junior Member
    Joined
    Mar 2008
    Posts
    67

    Question final ans...

    umm.. for the final answer i got 1/6 m/min for dD/dt, is tha right?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by a.a View Post
    umm.. for the final answer i got 1/6 m/min for dD/dt, is tha right?
    Yes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 23rd 2010, 03:43 PM
  2. related rates questions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 14th 2010, 03:51 AM
  3. Related Rates Questions..
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 12th 2010, 06:55 PM
  4. Related Rates Questions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 2nd 2009, 03:57 PM
  5. rates and related rates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 29th 2007, 09:51 PM

Search Tags


/mathhelpforum @mathhelpforum