- #1

karush

Gold Member

MHB

- 3,269

- 5

$\tiny{2.8.1}$

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

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

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