anonymous
  • anonymous
Help Please!! Air is being pumped into a leaking spherical balloon at the rate of 30π cm3/sec. If the radius of the balloon is increasing by 0.1 cm/sec, find the leakage rate, R, when the radius of the balloon is 5 cm.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
The first three things you need to do is find an equation for the volume of the sphere given its current radius, then find an equation for the rate of change of the volume in the sphere. Finally, use both of these to find the rate of change of the radius given a volume.
anonymous
  • anonymous
so would the answer be 3570π??
anonymous
  • anonymous
Not quite what I got. How did you put the steps together?

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anonymous
  • anonymous
i have the equation set up to dv/dt=4pir ^{3} then plug in 30pi for r
anonymous
  • anonymous
then get dv/dt=3600π
anonymous
  • anonymous
So: \[ \begin{align*} V(t) &= \frac{4}{3}\pi r^3\\ \frac{dV}{dt} &= 4\pi r^2 \frac{dr}{dt} \end{align*} \] You need to plug in what you got for what \(\frac{dV}{dt}\) is and then plug in the numbers you're given to solve for \(R\).

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