Question: A thin, circular plate in a boiler is expanding so that its radius is changing 0.01 cm/s. How fast is the area of one face changing when the radius is 5cm?

Here is my working, I'm I on the right track so far?

$\displaystyle A=\pi r^2$

$\displaystyle \frac{dA}{dt}=2\pi r \cdot \frac{dr}{dt}$

$\displaystyle \frac{dA}{dt}= 2\pi (5) \cdot 0.01$

$\displaystyle \frac{dA}{dt}= 0.314$ (this is for 2 plates - is this correct?)

Therefore, $\displaystyle \frac{0.314}{2} = 0.157 cm/s$ (is this correct?)