Math — Related Rates

\frac{dV}{dt} = \frac{dV}{dr}\frac{dr}{dt}

\frac{d}{dt}(x^2 + y^2) = 2x\dot{x} + 2y\dot{y}

A = \pi r^2 \Rightarrow \frac{dA}{dt} = 2\pi r\frac{dr}{dt}

\text{differentiate, then substitute}