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Math Help - Rate air leaks from balloon.

  1. #1
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    Rate air leaks from balloon.

    A spherical balloon with an initial radius r of 5 inches begins to leak at time t = 0, and its radius t seconds later is r = (60-t)/12in. At what rate (in cubic inches/second) is air leaking from the balloon when t = 30?

    Please help!
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  2. #2
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    Quote Originally Posted by poitier View Post
    A spherical balloon with an initial radius r of 5 inches begins to leak at time t = 0, and its radius t seconds later is r = (60-t)/12in. At what rate (in cubic inches/second) is air leaking from the balloon when t = 30?

    Please help!
     <br />
V = \frac{4}{3}\pi r^3<br />

    \frac{dV}{dt} = 4\pi r^2 \cdot \frac{dr}{dt}

    at t = 30 sec ...

     <br />
\frac{dV}{dt} = 4\pi (2.5)^2 \cdot \left(-\frac{1}{12}\right)<br />
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  3. #3
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    Thank you! That helps a lot. But how do I find dr/dt? How do I know that it equals (-1/12)?
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  4. #4
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    Hi poitier,

    differentiate your given formula for r with respect to t.

    This isn't one of those balloons that start off spherical and up end sausage-shaped as the air escapes i hope!
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