Question

what is the radius of the circle increases at the rate of 0.01 inch per second, find the rate of change of the area when the radius is 3 inches long

Answer 1

We know that the area of the circle determine as $S=πr^2.$ Also we have $\frac{dr}{dt}=0.01$ in/sec, because the radius of the circle increases at the rate of 0.01 in per second.

Find $\frac{dS}{dt}=2πr\frac{dr}{dt}.$

Such as r=3 in, then

 $\frac{dS}{dt}=2π•3•0.01=0.06π$ in²/sec or 0.1884 in²/sec

Answer. 0.1884 in²/sec