Question

question. the radius of a circle increases at a rate of 1/2 m/s. find the rate, in m²/s, at which the area of the circle is increasing when the radius is 7 m. answer in terms of π. do not include 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 given values

$r = 7$, $\frac{dr}{dt}=\frac{1}{2}$, so $\frac{dA}{dt}=2\pi\times7\times\frac{1}{2}$

Answer:

$7\pi$