Answer to Question #250368 in Calculus for red

Question

1. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change of the area when the radius is 3 cm long

Answer 1

Solution.

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

Find $\frac{dS}{dt}=2πr\frac{dr}{dt}.$ Such as r=3 cm, then $\frac{dS}{dt}=2π•3•0.01=0.06π$ cm²/sec or 0.1884 cm²/sec.

Answer. 0.1884 cm²/sec