A spherical ball of salt is dissolving in water

You have $V=\frac{4}{3} \pi r^3$ so: $$\frac{d V}{dt}=\frac{d}{dt}\left(\frac{4}{3} \pi r^3 \right)=\frac{4}{3} \pi \times 3 \frac{dr}{dt} r^2 $$ so the equation is: $$4 \pi \frac{dr}{dt} r^2 = k 4 \pi r^2$$ i.e (as long as $r\neq 0$): $$\frac{dr}{dt}=k$$.