Question

question a circle has a radius that is increasing at a rate of 9/π feet per second. what is the rate of change of the area of the circle when the radius is 3 feet? (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

Given $r = 3$ and $\frac{dr}{dt}=\frac{9}{\pi}$, then $\frac{dA}{dt}=2\pi\times3\times\frac{9}{\pi}$

Step4: Simplify

$\frac{dA}{dt}=54$

Answer:

54