Question

the radius of a circle is increasing at a steady rate of 6 cm/min. how fast is the area of the circle increasing when the radius is 5 cm?
$\frac{da}{dt}=$ symbolic expression $equiv$ $cm^{2}/min$
save & grade 5 attempts left save only
10 points available for this attempt (following attempts are worth: 9, 8, 6, 3)

Explanation:

Step1: Recall area formula of circle

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius.

Step2: Differentiate with respect to time $t$

Using the chain - rule, $\frac{dA}{dt}=2\pi r\frac{dr}{dt}$.

Step3: Substitute given values

We know that $\frac{dr}{dt}=6$ cm/min and $r = 5$ cm. Substitute these values into the derivative formula: $\frac{dA}{dt}=2\pi\times5\times6$.

Step4: Calculate the result

$\frac{dA}{dt}=60\pi$ $cm^{2}/min$.

Answer:

$60\pi$