Question

Let A be the area of a circle with radius r. If dr/dt=3, find dA/dt when r=2.

Answer 1

Area=pir^2
take deritivive
dA/dt=2pir (dr/dt)
given dr/dt=3
dA/dt=2pi(2)(3)
dA/dt=12pi

Answer 2

$\bf \textit{area of a circle}=A=\pi r^2 \\\\\\ \cfrac{dA}{dt}=\pi \cdot 2r^1\cdot \cfrac{dr}{dt}\implies \cfrac{dA}{dt}=\pi \cdot 2r\cdot \cfrac{dr}{dt}\quad \begin{cases} r=2\\ \frac{dr}{dt}=3 \end{cases} \\\\\\ \cfrac{dA}{dt}=\pi \cdot 2(2)(3)$