How fast is the area of the square increasing when the radius is 30m?

Given: $\displaystyle \frac{dx}{dt} = 6 cm/s$

Required: $\displaystyle \frac{dA}{dt}$ when $\displaystyle \frac{dr}{dt}$

Solution: Let $A = x^2$ be the area of square where $x$ = side of the square

$\displaystyle \frac{dA}{dt} = \frac{dA}{dx} \left( \frac{dx}{dt} \right) = 2 x \frac{dx}{dt} $

$\displaystyle \frac{dA}{dt} = 2x \frac{dx}{dt}$

To get the value of $x$, we use the given area to get $x$

$ \begin{equation} \begin{aligned} A =& x^2 \\ \\ x =& \sqrt{A} ; A = 16 \\ \\ \frac{dA}{dt} =& 2 (4)(6) \\ \\ \end{aligned} \end{equation} $

$\fbox{$\large \frac{dA}{dt} = 48 cm^2 /s $}$

Posted on

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now