# Rate air leaks from balloon.

• Feb 8th 2010, 09:41 AM
poitier
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?

• Feb 8th 2010, 10:51 AM
skeeter
Quote:

Originally Posted by poitier
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?

$
V = \frac{4}{3}\pi r^3
$

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

at t = 30 sec ...

$
\frac{dV}{dt} = 4\pi (2.5)^2 \cdot \left(-\frac{1}{12}\right)
$
• Feb 8th 2010, 12:15 PM
poitier
Thank you! That helps a lot. But how do I find dr/dt? How do I know that it equals (-1/12)?
• Feb 8th 2010, 01:16 PM