Question

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.

Answer 1

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.

Answer 2

so would the answer be 3570π??

Answer 3

Not quite what I got. How did you put the steps together?

Answer 4

i have the equation set up to dv/dt=4pir ^{3}
then plug in 30pi for r

Answer 5

then get dv/dt=3600π

Answer 6

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 \(R\).