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
