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Math Help - Balloon's growth speed

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    29

    Balloon's growth speed

    Need help with this task =/

    Dad is blowing up a balloon for his son so that the volume of the balloon is growing 1 litre per second. How fast is the ball growing, when
    a) the balloon's volume is 4 litres
    b) the balloon's diameter is 30 cm ?

    I know that I can calculate the volume of the balloon with
    V(r) = 4/3pi*r^3
    I also assume the ball's growth speed can be calculated by using
    V'(r) = 4pi*r^2 ?
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  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    The volume V may also be written as a function of t. In that case, the rate of change becomes

    V'(t)=\frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)=4\pi r^2\frac{dr}{dt}.
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