Answer to Question #281355 in Calculus for eunice

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