Surface area of a sphere: $A=4\pi r^2$ Volume of a sphere: $V=\dfrac43\pi r^3$ Differentiate both with respect to an arbitrary variable for time: $\displaystyle\frac{\mathrm dA}{\mathrm dt}=8\pi r\frac{\mathrm dr}{\mathrm dt}$ $\displaystyle\frac{\mathrm dV}{\mathrm dt}=4\pi r^2\frac{\mathrm dr}{\mathrm dt}$ You're given that $\dfrac{\mathrm dA}{\mathrm dt}=-3\pi$ when $r=2$, so you can use this in the first equation to solve for $\dfrac{\mathrm dr}{\mathrm dt}$. $-3\pi=8\pi \times2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=-\dfrac3{16}$ Now use this to find $\dfrac{\mathrm dV}{\mathrm dt}$. $\displaystyle\frac{\mathrm dV}{\mathrm dt}=4\pi \times2^2\times\left(-\dfrac3{16}\right)=-3\pi$