MHB Apc.2.8.1 ap vertical circular cylinder related rates

[karush]

$\tiny{2.8.1}$

The vertical circular cylinder has radius r ft and height h ft.
If the height and radius both increase at the constant rate of 2 ft/sec,
Then what is the rate at which the lateral surface area increases?
\een
$\begin{array}{ll}
a&4\pi r\\
b&2\pi(r+h)\\
c&4\pi(r+h)\\
d&4\pi rh\\
e&4\pi h
\end{array}$
ok here is my setup
\begin{array}{lll}
\textit{given rates}
&\dfrac{dr}{dt}=2 \quad \dfrac{dh}{dt}=2
&(1)\\ \\
\textit{surface area eq}
&2\pi rh
&(2)\\ \\
\end{array}
so far

 

[skeeter]

$\dfrac{dA}{dt} = 2\pi\left(r \cdot \dfrac{dh}{dt} + h \cdot \dfrac{dr}{dt} \right)$

 

[karush]

$\dfrac{dA}{dt} = 2\pi\left(r \cdot \dfrac{dh}{dt} + h \cdot \dfrac{dr}{dt} \right) =2\pi(2r+2h)=4\pi(r+h)$