# Thread: Rate air leaks from balloon.

1. ## 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?

2. 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?

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

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

at t = 30 sec ...

$\displaystyle \frac{dV}{dt} = 4\pi (2.5)^2 \cdot \left(-\frac{1}{12}\right)$

3. Thank you! That helps a lot. But how do I find dr/dt? How do I know that it equals (-1/12)?

4. 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!