Question

question a circle has a radius that is decreasing at a rate of $\frac{18}{pi}$ mm per minute. what is the rate of change of the area of the circle when the radius is 4 mm? (do not include the units in your answer.) provide your answer below:

Explanation:

Step1: Recall area formula

$A = \pi r^{2}$

Step2: Differentiate with respect to time

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

Step3: Substitute values

$r = 4$, $\frac{dr}{dt}=-\frac{18}{\pi}$, so $\frac{dA}{dt}=2\pi\times4\times(-\frac{18}{\pi})$

Step4: Calculate result

$\frac{dA}{dt}=-144$

Answer:

$-144$