The volume of a spherical balloon is decreasing at a rate of $20 cm^3/min$. How fast is the radius of the balloon decreasing when the volume is $1m^3$?
Basically I did this:
$V=\frac 43\pi r^3$
When the volume is $1m^3$, $r=\sqrt[3] {3000000 cm^3 \over 4\pi}$
Then I implicitly derived the volume equation and got:
${dV \over dt} = 4\pi r^2 {dr\over dt}$
Then I replaced
$ 20 {cm^3 \over min} = 4\pi \sqrt[2/3] {3000000 cm^3 \over 4\pi} {dr \over dt}$
And solving for ${dr \over dt}$ I finally got approximately $0.54 cm/min$
I'm not sure if it's right, or not. And I'm not sure if the final answer should have a minus sign since the radius -and the volume obviously- is decreasing.