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

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