A balloon is being filled with helium at the rate of $4\frac{ft^3}{min}$. The rate, in feet per minute, at which the radius is increasing when the radius is $2$ feet is ($V=\frac43 \pi r^3$): ?
I know rate of change has to do with derivatives but after finding the derivative of the volume equation I don't know what to do next.
I don't want the answer to this specific problem, I don't understand how to do these specific problems in general.
Best Answer
hint: $\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt}$, and you are given: $\dfrac{dV}{dt} = 4, r = 2$, can you find $\dfrac{dr}{dt}$ ?