I need some help on this problem. A snowball is melting at the rate of $\displaystyle 6.00\; \frac{cm^3}{min}$ If it remains spherical, how fast is the radius decreasing when the radius is $\displaystyle 2.00\; cm$ ?
the volume of a sphere is given by:
$\displaystyle V = \frac 43 \pi r^3$
differentiate implicitly with respect to t (time)
$\displaystyle \Rightarrow \frac {dV}{dt} = 4 \pi r^2 \frac {dr}{dt}$
you are given dV/dt (note that this is negative) and r, you want dr/dt, so solve for it
you are given that $\displaystyle \frac{dV}{dt}=-6$...now by using $\displaystyle V_{sphere}=\frac{4}{3}\pi{r^3}$...we have our equation...differntiating we get $\displaystyle \frac{dV}{dt}=4\pi{r^2}\cdot{dr}{dt}$...we know the values of $\displaystyle \frac{dV}{dt}$ and $\displaystyle r$ so plug and solve