Question

He radius r of a circle is increasing at a rate of 6 centimeters per minute. find the rate of change of the area when r = 35 centimeters. cm2/min

Answer 1

You can solve this problem by following the steps below:

 1. You need the formula for calculate the area of a circle, which is:

 A=πr²

 "A" is the area of the circle
 "r" is the radius of the circle (r=35 centimeters).

 2. Now, you must take the derivative. Then, the rate of change of the area is:

 dA/dt=(2πr)(dr/dt)

 3. The radius of change of the radius "r" with respect to time, is:

 dr/dt=6 cm/min

 4. Then, you have:

 dA/dt=(2πr)(dr/dt)
 dA/dt=2π(35 cm)(6 cm/min)
 dA/dt=420π cm²/min